Tính \(S=\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2}+\frac{1}{3}\right)\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)+...+\left(1+\frac{1}{2}+...+\frac{1}{10}\right)\)
Các bạn giúp mình nhé !~~~
Những câu hỏi liên quan
\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{7}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
Giúp mình với, mình đang cần gấp lắm nhé các bạn!
left(frac{-5}{12}+frac{7}{4}-frac{3}{8}right)-left[4frac{1}{2}-7frac{1}{3}right]-left(frac{1}{4}-frac{5}{2}right)left[2frac{1}{4}-5frac{3}{2}right]-left(frac{3}{10}-1right)-5frac{1}{2}+left(frac{1}{3}-frac{5}{6}right)frac{4}{7}-left(3frac{2}{5}-1frac{1}{2}right)-frac{5}{21}+left[3frac{1}{2}-4frac{2}{3}right]frac{1}{8}-1frac{3}{4}+left(frac{7}{8}-3frac{7}{2}+frac{3}{4}right)-left[frac{7}{4}-frac{5}{8}right]left(frac{3}{5}-2frac{1}{10}+frac{11}{20}right)-left[frac{-3}{4}+1frac{7}{2}right]left[-2fr...
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\(\left(\frac{-5}{12}+\frac{7}{4}-\frac{3}{8}\right)-\left[4\frac{1}{2}-7\frac{1}{3}\right]-\left(\frac{1}{4}-\frac{5}{2}\right)\)
\(\left[2\frac{1}{4}-5\frac{3}{2}\right]-\left(\frac{3}{10}-1\right)-5\frac{1}{2}+\left(\frac{1}{3}-\frac{5}{6}\right)\)
\(\frac{4}{7}-\left(3\frac{2}{5}-1\frac{1}{2}\right)-\frac{5}{21}+\left[3\frac{1}{2}-4\frac{2}{3}\right]\)
\(\frac{1}{8}-1\frac{3}{4}+\left(\frac{7}{8}-3\frac{7}{2}+\frac{3}{4}\right)-\left[\frac{7}{4}-\frac{5}{8}\right]\)
\(\left(\frac{3}{5}-2\frac{1}{10}+\frac{11}{20}\right)-\left[\frac{-3}{4}+1\frac{7}{2}\right]\)
\(\left[-2\frac{1}{5}-2\frac{2}{3}\right]-\left(\frac{1}{15}-5\frac{1}{2}\right)+\left[\frac{-1}{6}+\frac{1}{3}\right]\)
\(1\frac{1}{8}-\left(\frac{1}{15}-\frac{1}{2}+\frac{-1}{6}\right)+\left[\frac{5}{4}+\frac{3}{2}\right]\)
\(\frac{5}{6}-\left(1\frac{1}{3}-1\frac{1}{2}\right)+\left[\frac{5}{12}-\frac{3}{4}-\frac{1}{6}\right]\)
\(1\frac{1}{4}-\left(\frac{7}{12}-\frac{2}{3}-1\frac{3}{8}\right)+\left[\frac{5}{24}-2\frac{1}{2}\right]-\frac{1}{6}-\left[\frac{-3}{4}\right]\)
\(-2\frac{1}{5}+2\frac{3}{10}-\left(\frac{6}{20}-\left[\frac{2}{8}-1\frac{1}{2}\right]\right)+\left[\frac{7}{20}-1\frac{1}{4}\right]\)
\(-\left[1\frac{2}{3}-3\frac{1}{2}+\frac{1}{4}\right]+\left(\frac{2}{6}-\frac{5}{12}\right)-\left(\frac{1}{3}-\left[\frac{1}{4}-\frac{1}{3}\right]\right)\)
\(-\frac{4}{5}-\left(1\frac{1}{10}-\frac{7}{10}\right)+\left[\frac{3}{4}-1\frac{1}{5}\right]+1\frac{1}{2}\)
\(\frac{3}{21}-\frac{5}{14}+\left[1\frac{1}{3}-5\frac{1}{2}+\frac{5}{14}\right]-\left(\frac{1}{6}-\frac{3}{7}+\frac{1}{3}\right)\)
\(-1\frac{2}{5}+\left[1\frac{3}{10}-\frac{7}{20}-1\frac{1}{4}\right]-\left(\frac{1}{5}-\left[\frac{3}{4}-1\frac{1}{2}\right]\right)\)
\(2\frac{1}{3}-\left(\frac{1}{2}-2\frac{1}{6}+\frac{3}{4}\right)+\left[\frac{5}{12}-1\frac{1}{3}\right]-\frac{7}{8}+3\frac{1}{2}\)
\(2\frac{1}{4}-1\frac{3}{5}-\left(\frac{9}{20}-\frac{7}{10}\right)+\left[1\frac{3}{5}-2\frac{1}{2}\right]+\frac{3}{4}\)
\(\left[\frac{8}{3}-5\frac{1}{4}+\frac{1}{6}\right]-\frac{7}{4}+\frac{-5}{12}-\left(1-1\frac{1}{2}+\frac{1}{3}\right)\)
\(\left(\frac{1}{4}-\left[1\frac{1}{4}-\frac{7}{10}\right]+\frac{1}{2}\right)-2\frac{1}{5}-1\frac{3}{10}+\left[1-\frac{1}{2}\right]\)
TRÌNH BÀY GIÚP MÌNH NHA
\(F=\frac{\left(\frac{53}{4}-2\frac{5}{27}-\frac{65}{6}\right).\left(230+\frac{1}{25}\right)+46\frac{3}{4}}{\left(\frac{24}{7}+3\frac{1}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
giúp mình nhé các bạn
Tính tổng S=\(\sqrt{1+\left(1+\frac{1}{3}\right)^2}+\sqrt{1+\left(\frac{1}{2}+\frac{1}{4}\right)^2}+\sqrt{1+\left(\frac{1}{3}+\frac{1}{5}\right)^2}+...+\sqrt{1+\left(\frac{1}{48}+\frac{1}{50}\right)^2}\)
giúp mình với
6.b) A=\(\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)+\left(1+\frac{1}{4}\right)\times..........\times\left(1+\frac{1}{99}\right)=\)Các bạn giúp mình nhanh và đúng nhé mình tick cho bạn đầu tiên nhé
\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)
\(=\frac{3}{2}\times\frac{4}{3}\times...\times\frac{100}{99}\)
\(=\frac{100}{2}=50\)
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Tính:
\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)....\left(1-\frac{1}{10^2}\right)\)
Các CTV giải giúp mình với nha.
Ta có :
\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right).....\left(1-\frac{1}{10^2}\right)\)
\(=\)\(\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}.....\frac{10^2-1}{10^2}\)
\(=\)\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{9.11}{10.10}\)
\(=\)\(\frac{1.3.2.4.3.5.....9.11}{2.2.3.3.4.4.....10.10}\)
\(=\)\(\frac{\left(1.2.3.....9\right).\left(3.4.5.....11\right)}{\left(2.3.4.....10\right).\left(2.3.4.....10\right)}\)
\(=\)\(\frac{11}{2.10}\)
\(=\)\(\frac{11}{20}\)
Chúc bạn học tốt ~
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(1-1/2^2)(1-1/3^2)(1-1/4^2)....(1-1/10^2)
=3/4.8/9.15/16...99/100
Từ đó tính kết quả là ok
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\(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)..\left(1-\frac{1}{10^2}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{99}{100}\)=\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{9.11}{10.10}\)
\(=\frac{1.2.3...9}{2.3.4...10}.\frac{3.4.5...11}{2.3.4...10}\)\(=\frac{1}{10}.\frac{11}{2}=\frac{11}{20}\)
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1, Tính giá trị biểu thức :
\(a,A=5\frac{9}{10}:\frac{3}{2}-\left(2\frac{1}{3}.4\frac{1}{2}-2.2\frac{1}{3}\right):\frac{7}{4}\)
\(b,B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).............\left(1-\frac{1}{2017}\right).\left(1-\frac{1}{2018}\right)\)
Mọi người giúp mình giả toán nha !
Ta có:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)........\left(1-\frac{1}{2017}\right).\left(1-\frac{1}{2018}\right)\)
\(\Rightarrow B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{2016}{2017}.\frac{2017}{2018}\)
Đởn giản hết sẽ còn là:
\(\Rightarrow B=\frac{1}{2018}\)
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tính A biết
A=\(\left(\frac{1}{1+2}-1\right)\times\left(\frac{1}{1+2+3}-1\right)\times\left(\frac{1}{1+2+3+4}-1\right)\times...\times\left(\frac{1}{1+2+3+4+...+2018}-1\right)\)
Giúp mình nhanh nha các bạn
Thực hiện phép tính :a, sqrt{12frac{1}{4}}.left(-frac{2}{7}right)^2-left[2,left(4right).2frac{5}{11}right]:(-frac{42}{5})b, left(1-frac{1}{2}right).left(1-frac{1}{3}right).left(1-frac{1}{4}right)...left(1-frac{1}{2007}right)c, 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}Các bạn giải nhanh giúp mình nha!
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Thực hiện phép tính :
a, \(\sqrt{12\frac{1}{4}}.\left(-\frac{2}{7}\right)^2-\left[2,\left(4\right).2\frac{5}{11}\right]:(-\frac{42}{5})\)
b, \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2007}\right)\)
c, \(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{-0,625+0,5-\frac{5}{11}-\frac{5}{12}}+\frac{1,5+1-0,75}{2,5+\frac{5}{3}-1,25}\)
Các bạn giải nhanh giúp mình nha!