\(\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{47.50}\)
\(=\frac{4}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{47.50}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{47}-\frac{1}{50}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{5}-\frac{1}{50}\right)\)
\(=\frac{4}{3}.\left(\frac{10}{50}-\frac{1}{50}\right)\)
\(=\frac{4}{3}.\frac{9}{50}\)
\(=\frac{6}{25}\)
4/5x8 + 4/8x11 + ... + 4/47x50
= 4/3 (3/5x8 + 3/8x11 + ... + 3/47x50)
= 4/3 (1/5 - 1/8 + 1/8 - 1/11 + ... + 1/47 -1/50)
= 4/3 (1/5 - 1/50)
= 4/3 . 9/50
= 6/25
gọi tổng trên là a ta có :
A x 3/4=3/5x8 + 3/8x11 + .....+3/47x50
=1/5 - 1/8 + 1/8 - 1 /11 + ......+ 1/47 - 1/50
= 1/5 - 1/50
= 9/50
=9/50 : 3/4
= 6/25
\(\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{47.50}\)
\(=\frac{4}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{47.50}\right)\)
\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{47}-\frac{1}{50}\right)\)
\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{50}\right)\)
\(=\frac{4}{3}.\frac{9}{50}=\frac{6}{25}\)