\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+;;;;+\frac{1}{110}\)
AI NHANH TAY TICK 5 LAI NHE !
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19 tháng 8 2019 lúc 11:16
e,Afrac{1}{2}+frac{5}{6}+frac{11}{12}+frac{19}{20}+frac{29}{30}+frac{41}{42}left(1-frac{1}{2}right)+left(1-frac{1}{6}right)+left(1-frac{1}{12}right)+left(1-frac{1}{20}right)+left(1-frac{1}{20}right)+left(1-frac{1}{42}right)Rightarrow A1-frac{1}{2}+1-frac{1}{6}+1-frac{1}{12}+1-frac{1}{20}+1-frac{1}{30}+1-frac{1}{42}4-left(frac{1}{2}+frac{1}{6}+frac{1}{12}+frac{1}{20}+frac{1}{30}+frac{1}{42}right)Rightarrow A4-left(frac{1}{1.2}+frac{1}{2.3}+frac{1}{3.4}+frac{1}{4.5}+frac{1}{5.6}+frac{1}{6.7}right)...
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e,\(A=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{42}\right)\)
\(\Rightarrow A=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}=4-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(\Rightarrow A=4-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=4-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(\Rightarrow A=4-\left(\frac{1}{1}-\frac{1}{7}\right)=4-\frac{6}{7}=3\frac{1}{7}\)
BN mún hỏi j vậy, đây k phải câu hỏi, mà có thì phải là toán lớp 6
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Dưới đây là lời giải chi tiết và sửa lỗi cho bài toán của bạn:
Bài toán: Tính giá trị biểu thức\(A = \frac{1}{2} + \frac{5}{6} + \frac{11}{12} + \frac{19}{20} + \frac{29}{30} + \frac{41}{42}\)
Bước 1: Biến đổi từng phân sốMỗi phân số có thể viết dưới dạng:
\(\frac{1}{2} = 1 - \frac{1}{2} , \frac{5}{6} = 1 - \frac{1}{6} , \frac{11}{12} = 1 - \frac{1}{12} , \frac{19}{20} = 1 - \frac{1}{20} , \frac{29}{30} = 1 - \frac{1}{30} , \frac{41}{42} = 1 - \frac{1}{42}\)Vậy:
\(A = \left(\right. 1 - \frac{1}{2} \left.\right) + \left(\right. 1 - \frac{1}{6} \left.\right) + \left(\right. 1 - \frac{1}{12} \left.\right) + \left(\right. 1 - \frac{1}{20} \left.\right) + \left(\right. 1 - \frac{1}{30} \left.\right) + \left(\right. 1 - \frac{1}{42} \left.\right)\)Bước 2: Tổng hợp các số hạngCó 6 số hạng dạng \(1\), nên:
\(A = 6 - \left(\right. \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42} \left.\right)\)Bước 3: Tính tổng trong ngoặcNhận xét:
\(\frac{1}{n \left(\right. n + 1 \left.\right)} = \frac{1}{n} - \frac{1}{n + 1}\)Áp dụng:
\(\frac{1}{2} = \frac{1}{1 \cdot 2} = 1 - \frac{1}{2}\)\(\frac{1}{6} = \frac{1}{2 \cdot 3} = \frac{1}{2} - \frac{1}{3}\)\(\frac{1}{12} = \frac{1}{3 \cdot 4} = \frac{1}{3} - \frac{1}{4}\)\(\frac{1}{20} = \frac{1}{4 \cdot 5} = \frac{1}{4} - \frac{1}{5}\)\(\frac{1}{30} = \frac{1}{5 \cdot 6} = \frac{1}{5} - \frac{1}{6}\)\(\frac{1}{42} = \frac{1}{6 \cdot 7} = \frac{1}{6} - \frac{1}{7}\)Cộng tất cả lại:
\(\left(\right. 1 - \frac{1}{2} \left.\right) + \left(\right. \frac{1}{2} - \frac{1}{3} \left.\right) + \hdots + \left(\right. \frac{1}{6} - \frac{1}{7} \left.\right) = 1 - \frac{1}{7}\)Bước 4: Tính giá trị \(A\)Thay vào công thức:
\(A = 6 - \left(\right. 1 - \frac{1}{7} \left.\right) = 6 - \frac{6}{7} = \frac{36}{7} = 5 \frac{1}{7}\)Sửa lỗi trong đề bàiBạn đã nhầm 6 số hạng thành 4 số hạng ở bước tổng hợp. Kết quả chính xác là:
\(\boxed{A = \frac{36}{7} \approx 5.1429}\)Giải thích này đã rõ chưa bạn? 😊
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kiểm tra hộ em
1/ thực hiện phép tính
a/\(\frac{1}{4}.\frac{2}{3}-\frac{3}{2}.\frac{1}{6}+\frac{1}{12}\)
=\(\frac{1}{6}-\frac{1}{4}+\frac{1}{12}\)
=\(\frac{2-3+1}{12}=\frac{-1+1}{12}=0\)
SGK Chân trời sáng tạo trang 58
2 tháng 11 2023 lúc 16:20
Tính.
a) $\frac{1}{3} + \frac{1}{3} + \frac{1}{6}$
b) $\frac{1}{{12}} + \frac{3}{4} + \frac{2}{{12}}$
c) $\frac{{19}}{{15}} + 0 + \frac{{11}}{{15}}$
a) $\frac{1}{3} + \frac{1}{3} + \frac{1}{6} = \frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6}$
b) $\frac{1}{{12}} + \frac{3}{4} + \frac{2}{{12}} = \left( {\frac{1}{{12}} + \frac{2}{{12}}} \right) + \frac{3}{4} = \frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1$
c) $\frac{{19}}{{15}} + 0 + \frac{{11}}{{15}} = \frac{{19 + 11}}{{15}} = \frac{{30}}{{15}} = 2$
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tính A = \(\frac{\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}}{5+\frac{5}{3}+\frac{5}{6}+\frac{1}{2}+...+\frac{1}{9}}\)
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right)×\left(\frac{1}{3}+\frac{1}{2}-\frac{5}{6}\right)\)
Ta có:
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right).\left(\frac{1}{3}+\frac{1}{2}-\frac{5}{6}\right)\)
\(=\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right).\left(\frac{5}{6}-\frac{5}{6}\right)\)
\(=\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right).0\)
\(=0\)
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Ta có:
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right).\left(\frac{1}{3}+\frac{1}{2}-\frac{5}{6}\right)\)
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right).\left(\frac{5}{6}-\frac{5}{6}\right)\)
\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1100}\right).0\)
\(=0\)
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Tính nhanh (nếu có thể):
a,frac{frac{3}{41}-frac{12}{47}+frac{27}{53}}{frac{4}{41}-frac{16}{47}+frac{36}{53}}+frac{-0,25.frac{-2}{3}-75%:(frac{-1}{2}+frac{2}{3})}{|-1frac{1}{2}|.(frac{-2}{3}-0,75:frac{3}{-2})}
b,A158.(frac{12-frac{12}{7}-frac{12}{289}-frac{12}{85}}{4-frac{4}{7}-frac{4}{289}-frac{4}{85}}:frac{5+frac{5}{13}+frac{5}{169}+frac{5}{91}}{6+frac{6}{13}+frac{6}{169}+frac{6}{91}}).frac{50550505}{711711711}
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Tính nhanh (nếu có thể):
\(a,\frac{\frac{3}{41}-\frac{12}{47}+\frac{27}{53}}{\frac{4}{41}-\frac{16}{47}+\frac{36}{53}}+\frac{-0,25.\frac{-2}{3}-75\%:(\frac{-1}{2}+\frac{2}{3})}{|-1\frac{1}{2}|.(\frac{-2}{3}-0,75:\frac{3}{-2})}\)
\(b,A=158.(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}).\frac{50550505}{711711711}\)
a: \(=\dfrac{3\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}{4\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}+\dfrac{-\dfrac{1}{4}\cdot\dfrac{-2}{3}-\dfrac{3}{4}:\dfrac{1}{6}}{\dfrac{3}{2}\cdot\left(\dfrac{-2}{3}-\dfrac{3}{4}\cdot\dfrac{-2}{3}\right)}\)
\(=\dfrac{3}{4}+\dfrac{\dfrac{2}{12}-\dfrac{9}{2}}{\dfrac{3}{2}\cdot\dfrac{-1}{6}}=\dfrac{3}{4}+\dfrac{-13}{3}:\dfrac{-3}{12}\)
\(=\dfrac{3}{4}+\dfrac{13}{3}\cdot\dfrac{12}{3}=\dfrac{3}{4}+\dfrac{156}{9}=\dfrac{217}{12}\)
b: \(A=158\left(\dfrac{12\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}{4\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}:\dfrac{5\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}{6\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}\right)\cdot\dfrac{50550505}{711711711}\)
\(=158\cdot\left(3\cdot\dfrac{6}{5}\right)\cdot\dfrac{50550505}{711711711}\)
\(\simeq40.39\)
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Tính nhanh (nếu có thể):a,frac{frac{3}{41}-frac{12}{47}+frac{27}{53}}{frac{4}{41}-frac{16}{47}+frac{36}{53}}+frac{-0,25.frac{-2}{3}-75%:(frac{-1}{2}+frac{2}{3})}{|-1frac{1}{2}|.(frac{-2}{3}-0,75:frac{3}{-2})}b,A158.(frac{12-frac{12}{7}-frac{12}{289}-frac{12}{85}}{4-frac{4}{7}-frac{4}{289}-frac{4}{85}}:frac{5+frac{5}{13}+frac{5}{169}+frac{5}{91}}{6+frac{6}{13}+frac{6}{169}+frac{6}{91}}).frac{50550505}{711711711}
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Tính nhanh (nếu có thể):
\(a,\frac{\frac{3}{41}-\frac{12}{47}+\frac{27}{53}}{\frac{4}{41}-\frac{16}{47}+\frac{36}{53}}+\frac{-0,25.\frac{-2}{3}-75\%:(\frac{-1}{2}+\frac{2}{3})}{|-1\frac{1}{2}|.(\frac{-2}{3}-0,75:\frac{3}{-2})}\)
\(b,A=158.(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}).\frac{50550505}{711711711}\)
3frac{1}{2}-4frac{2}{3}+left[frac{3}{4}-2frac{1}{3}right]-left(frac{5}{6}-frac{7}{4}right)+5frac{1}{2}-32frac{2}{3}-1frac{2}{5}+1frac{3}{10}-left(frac{2}{5}-frac{5}{6}right)+frac{4}{15}-1frac{1}{3}left[2frac{1}{3}-1frac{4}{3}right]-left(frac{5}{4}-frac{7}{12}+frac{-11}{6}right)+frac{4}{3}-frac{3}{4}-3frac{3}{2}+5frac{4}{3}-left(frac{7}{6}-1frac{3}{4}right)+left[frac{2}{3}-2frac{1}{4}right]2frac{2}{3}-frac{5}{12}-left(1frac{3}{4}-2frac{1}{4}right)-left[1-1frac{1}{6}right]+left[frac{-5}{3}right]1f...
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\(3\frac{1}{2}-4\frac{2}{3}+\left[\frac{3}{4}-2\frac{1}{3}\right]-\left(\frac{5}{6}-\frac{7}{4}\right)+5\frac{1}{2}-3\)
\(2\frac{2}{3}-1\frac{2}{5}+1\frac{3}{10}-\left(\frac{2}{5}-\frac{5}{6}\right)+\frac{4}{15}-1\frac{1}{3}\)
\(\left[2\frac{1}{3}-1\frac{4}{3}\right]-\left(\frac{5}{4}-\frac{7}{12}+\frac{-11}{6}\right)+\frac{4}{3}-\frac{3}{4}\)
\(-3\frac{3}{2}+5\frac{4}{3}-\left(\frac{7}{6}-1\frac{3}{4}\right)+\left[\frac{2}{3}-2\frac{1}{4}\right]\)
\(2\frac{2}{3}-\frac{5}{12}-\left(1\frac{3}{4}-2\frac{1}{4}\right)-\left[1-1\frac{1}{6}\right]+\left[\frac{-5}{3}\right]\)
\(1\frac{1}{3}-5\frac{1}{2}-\left[\frac{5}{6}-2\frac{2}{3}\right]+\left[\frac{7}{12}-\frac{5}{6}\right]\)
\(\frac{8}{15}-\left(\frac{2}{5}-3\frac{1}{3}+\left[\frac{-5}{6}\right]\right)+\left[\frac{1}{2}-\frac{4}{5}\right]-\left(\frac{1}{6}-1\frac{1}{3}\right)\)
\(-2\frac{3}{2}+\left[\frac{5}{6}-1\frac{1}{3}\right]-\left(\frac{5}{12}-\frac{7}{6}\right)+\left[\frac{4}{3}-3\frac{1}{4}\right]\)
\(\frac{9}{10}-1\frac{2}{5}-\left(\frac{5}{6}-3\frac{1}{2}\right)-\left[2\frac{1}{4}-5\frac{2}{36}\right]-\left[1-2\frac{1}{15}\right]\)
\(\frac{5}{7}-\frac{5}{21}+1\frac{2}{3}-\left(1\frac{1}{2}-\frac{5}{14}-\frac{1}{3}\right)+\left[\frac{1}{6}-\frac{4}{3}\right]\)
\(\frac{5}{7}-\frac{5}{21}+1\frac{2}{3}-\left(1\frac{1}{2}-\frac{5}{14}-\frac{1}{3}\right)+\left[\frac{1}{6}-\frac{4}{3}\right]\)
\(1\frac{1}{5}-\left(\frac{-9}{10}-2\frac{1}{2}+\frac{3}{4}\right)+\left[\frac{1}{5}-2\frac{1}{2}\right]+\frac{7}{10}-\left(\frac{1}{2}-\frac{1}{4}\right)\)
\(2\frac{1}{3}-\left(5\frac{1}{2}-2\frac{2}{3}\right)+\left[1\frac{1}{6}-2\frac{1}{2}\right]-\frac{5}{12}+\left(\frac{1}{4}-\frac{1}{8}\right)\)
29/152323/125/65/4-31/1231/6-13/31087/1801/61/62-67/24
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Ôi mẹ ơi dài khiếp
tính A = \(\frac{\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}}{5+\frac{5}{3}+\frac{5}{6}+\frac{1}{2}+...+\frac{1}{9}}\)
tks
tính
2,\(A=\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{-0,625+0,5-\frac{5}{11}-\frac{5}{12}}+\frac{1,5+1-0,75}{2,5+\frac{5}{3}-1,25}\)
3,\(B=\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}-\frac{2}{7}-\frac{2}{13}}.\frac{\frac{1}{3}-0,25+0,2}{1\frac{1}{6}-0,875+0,7}+\frac{6}{7}\)