Rút gọn: \(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+......+\frac{1}{20}\left(1+2+3+...+20\right)\)
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Rút gọn B=\(\left(1=\frac{1}{2}\right).\left(1=\frac{1}{3}\right).\left(1=\frac{1}{4}\right).....\left(1-\frac{1}{20}\right)\)
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\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)..................\left(1-\frac{1}{20}\right)\)
=\(\frac{1}{2}.\frac{2}{3}.............\frac{19}{20}\)
=\(\frac{1.2.3..............19}{2.3.4..............20}\)
=\(\frac{1}{20}\)
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Rút gọn : \(B=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)........\left(1+\frac{1}{20}\right)\)
\(B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{21}{20}\)
\(B=\frac{21}{2}\)
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\(B=\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{20}\right)\)
\(\Rightarrow B=\left(\frac{2}{2}+\frac{1}{2}\right)\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{4}{4}+\frac{1}{4}\right)...\left(\frac{20}{20}+\frac{1}{20}\right)\)
\(\Rightarrow B=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)
\(\Rightarrow B=\frac{21}{2}\)
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B=\(\left(1+\frac{1}{2}\right)\).\(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\)...\(\left(1+\frac{1}{20}\right)\)
B=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{21}{20}\)=\(\frac{21}{2}\)
vậy B= 21/2
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Xem thêm câu trả lời
RÚT GỌN B=\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{20}\right)\)
B=\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)
B=\(\frac{1.2.3....19}{2.3.4....20}\)
B=\(\frac{1}{20}\)
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Rút gọn: B=\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
Ta có:\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{20}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}=\frac{1}{20}\)
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Rút gọn:
A =\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
B = \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)
So sánh :
\(A=\frac{20^{10}+1}{20^{10}-1}vàB=\frac{20^{10}-1}{20^{10}-3}\)
Rút gọn :
a/ \(A=\frac{\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+...+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)
b/ \(B=\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right)...\left(1+\frac{2012}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{2012}\right)}\)
rút gọn : B= \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{20}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{19}{20}\)
\(=\frac{1\cdot2\cdot...\cdot19}{2\cdot3\cdot...\cdot20}\)
\(=\frac{1}{20}\)
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4 tháng 10 2017 lúc 20:50
1. Chứng minh : B left(1-frac{2}{6}right).left(1-frac{2}{12}right).left(1-frac{2}{20}right)...left(1-frac{2}{nleft(n+1right)}right)frac{1}{3}2. cho M frac{1}{1.left(2n-1right)}+frac{1}{3.left(2n-3right)}+frac{1}{5.left(2n-5right)}+...+frac{1}{left(2n-3right).3}+frac{1}{left(2n-1right).1}N 1+frac{1}{3}+frac{1}{5}+...+frac{1}{2n-1}Rút gọn frac{M}{N}
Đọc tiếp
1. Chứng minh : B = \(\left(1-\frac{2}{6}\right).\left(1-\frac{2}{12}\right).\left(1-\frac{2}{20}\right)...\left(1-\frac{2}{n\left(n+1\right)}\right)>\frac{1}{3}\)
2. cho M = \(\frac{1}{1.\left(2n-1\right)}+\frac{1}{3.\left(2n-3\right)}+\frac{1}{5.\left(2n-5\right)}+...+\frac{1}{\left(2n-3\right).3}+\frac{1}{\left(2n-1\right).1}\)
N = \(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2n-1}\)
Rút gọn \(\frac{M}{N}\)
Rút gọn: \(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
GIÚP MK VỚI !!!
\(B=\left[1-\frac{1}{2}\right]\cdot\left[1-\frac{1}{3}\right]\cdot\left[1-\frac{1}{4}\right]\cdot...\cdot\left[1-\frac{1}{20}\right]\)
\(B=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{19}{20}\)
\(B=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}=\frac{1}{20}\)
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