1/5.7 + 1/7.9 + 1/9.11 + ... + 1/49.51
= 1/2 . (2/5.7 + 2/7.9 + 2/9.11 + ... + 2/49.51)
= 1/2 . (1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + ... + 1/49 - 1/51)
= 1/2 . (1/5 - 1/51)
= 1/2 . 46/255
= 23/255
S = \(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...\frac{1}{49}-\frac{1}{51}\)
S = \(\frac{1}{5}-\frac{1}{51}=\frac{46}{255}\)
Đặt \(A=\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{49.51}\)
\(A.2=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{49.51}\)
\(A.2=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{49}-\frac{1}{51}\)
\(A.2=\frac{1}{5}-\frac{1}{51}\)
\(A.2=\frac{46}{255}\)
\(A=\frac{23}{255}\)
Đặt \(A=\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{49.51}\)
\(2A=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{49.51}\)
\(2A=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{49}-\frac{1}{51}\)
\(2A=\frac{1}{5}-\frac{1}{51}\)
\(A=\frac{46}{255}.\frac{1}{2}=\frac{23}{255}\)
Đặt \(A=\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{49.51}\)
\(A.2=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{49.51}\)
\(A.2=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{49}-\frac{1}{51}\)
\(A.2=\frac{1}{5}-\frac{1}{51}\)
\(A.2=\frac{46}{255}\)
\(A=\frac{23}{255}\)
= 1 / 5 - 1 / 7 + 1 / 7 - 1 / 9 + 1 / 9 - 1 /11 + .....+ 1 / 49 - 1 /51
= 1 / 5 - 1/ 51
= 46 / 255
\(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{49.50}\)
=\(\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{49.50}\right)\)
=\(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{49}-\frac{1}{50}\right)\)
=\(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{50}\right)\)
=\(\frac{1}{2}.\left(\frac{10}{50}-\frac{1}{50}\right)\)
=\(\frac{1}{2}.\frac{49}{50}\)
=\(\frac{49}{100}\)
k nha
\(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+....+\frac{1}{49.51}\)
\(=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{49.51}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{51}\right)\)
\(=\frac{1}{2}.\frac{46}{255}=\frac{23}{255}\)
\(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{49.51}\)
\(=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{51}\right)=\frac{1}{2}.\frac{46}{255}=\frac{23}{255}\)
Vậy tổng trên bằng \(\frac{23}{255}\)
K cho mk nha, mk làm nhanh nhất nhá
\(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{49.51}\)
\(=\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+....+\frac{2}{49.51}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{51}\right)\)
\(=\frac{1}{2}.\frac{46}{255}\)
\(=\frac{23}{255}\)
