rút gọn biểu thức:
g*) \(\frac{1489.1490+2978}{1492.1491-2984}\)
h*) \(\frac{6.134.2+12.163+4.203.3}{1+3+5+...+97+99-500}\)
hic, đau đầu quá :(((
Những câu hỏi liên quan
Bài 1 Rút gọn
B= \(\frac{1226395265}{1836547290}\)
E=\(\frac{2^4\cdot3^{15}+3\cdot561\cdot8+4\cdot124\cdot6}{1+3+5+7+...+97+99+500}\)
Cho A=\(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{49.51}}.\)Rút gọn A ta được A=.............
\(A=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{49.51}}\)Rút gọn A ta được A =
Rút gọn \(A=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{49.51}}\)
Giải
\(A=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+...+\frac{1}{49.51}}\)
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tính nhanh
\(A=\frac{1}{500}+\frac{3}{500}+\frac{5}{500}+...+\frac{95}{500}+\frac{97}{500}+\frac{99}{500}\)
\(A=\frac{1}{500}+\frac{3}{500}+\frac{5}{500}+...+\frac{95}{500}+\frac{97}{500}+\frac{99}{500}\)
\(A=\frac{1+3+5+...+95+97+99}{500}\)
\(A=\frac{\left(1+99\right)x50:2}{500}=\frac{100x50:2}{500}=\frac{100x5x10x\frac{1}{2}}{100x5}=10x\frac{1}{2}=5\)
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\(\frac{\frac{2000}{11}+\frac{2000}{12}+...+\frac{2000}{100}}{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{98}{2}+\frac{99}{1}}\)
Hãy rút gọn
Đặt \(A=\frac{\frac{2000}{11}+\frac{2000}{12}+...+\frac{2000}{100}}{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{98}{2}+\frac{99}{1}}\)
\(\Rightarrow A=\frac{2000.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{\left(1+\frac{1}{99}\right)+\left(1+\frac{2}{98}\right)+...+\left(1+\frac{98}{2}\right)+1}\)
\(\Rightarrow A=\frac{2000.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{\frac{100}{99}+\frac{100}{98}+...+\frac{100}{2}+\frac{100}{100}}\)
\(\Rightarrow A=\frac{2000.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{100.\left(\frac{1}{99}+\frac{1}{98}+...+\frac{1}{2}+\frac{1}{100}\right)}\)
\(\Rightarrow A=\frac{20.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{\frac{1}{99}+\frac{1}{98}+...+\frac{1}{2}+\frac{1}{100}}\)
\(\Rightarrow A=\frac{\frac{20}{11}+\frac{20}{12}+..+\frac{20}{100}}{\frac{1}{99}+\frac{1}{98}+..+\frac{1}{2}+\frac{1}{100}}\)
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Rút gọn P biết P = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\frac{97}{3}+...+\frac{1}{99}}\)
Cho A= \(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{97}+\frac{1}{99}}{\frac{1}{1.99}+\frac{1}{3.97}+\frac{1}{5.95}+....+\frac{1}{49.51}}\)rút gọn A ta được A=........
Rút gọn :
a, \(\frac{24.315+3.561.8+4.124.6}{1+3+5+7+...+97+99-500}\)
b, \(\frac{3^9.3^{20}.2^8}{3^{24}.243.2^6}\)
Trình bày đầy đủ ra .
Nhanh lên nhé ! Cần gấp !
a, \(\frac{24.315+3.561.8+4.124.6}{1+3+5+7+...+97+99-500}\) (1)
Đặt : S = 1 + 3 + 5 + 7 + ... + 97 + 99
SSH của S là : (99 -1) : 2 + 1 = 50(sh)
Tổng của S là : \(\frac{\left(99+1\right).50}{2}=\frac{100.50}{2}=\frac{5000}{2}=2500\)
Thay S vào biểu thức (1) Ta có :
\(\frac{24.315+3.561.8+4.124.6}{2500-500}\)
\(=\frac{3.8.315+3.561.8+4.2.124.3}{2000}\)
\(=\frac{3.8.315+3.561.8+8.124.3}{2000}\)
\(=\frac{\left(3.8\right).\left(315+561+124\right)}{2000}=\frac{24.1000}{2000}=\frac{24000}{2000}=12\)
b, \(\frac{3^9.3^{20}.2^8}{3^{24}.243.2^6}=\frac{3^{29}.2^8}{3^{24}.3^5.2^6}=\frac{3^{29}.2^6.2^2}{3^{29}.2^6}=2^2=4\)
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