Question

2 : [ 11.13 ] + 2 : [ 13.15 ] + 2 : [ 15.17 ] + ...+ 2 : [ 209.211]

Answer 1

\(\frac{2}{11.13}+\frac{2}{13.15}+.....+\frac{2}{209.211}\)

\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)\(+.....+\frac{1}{209}-\frac{1}{211}\)

\(=\frac{1}{11}-\frac{1}{211}=\frac{200}{2321}\)

hok tốt

Answer 2

Đặt \(A=\text{2 : [ 11.13 ] + 2 : [ 13.15 ] + 2 : [ 15.17 ] + ...+ 2 : [ 209.211]}\)

\(\Rightarrow A=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}...+\frac{2}{209.211}\)

\(\Rightarrow A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{209}-\frac{1}{211}\)

\(\Rightarrow A=\frac{1}{11}-\frac{1}{211}\)

\(\Rightarrow A=\frac{200}{2321}\)

~Study well~

Sai thì thôi nhé :D !

Answer 3

\(2:\left(11.13\right)+2:\left(13.15\right)+2:\left(15.17\right)+...+2:\left(209:211\right)\)

\(=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{209.211}\)

\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{209}-\frac{1}{211}\)

\(=\frac{1}{11}+\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{1}{15}-\frac{1}{15}\right)+...+\left(\frac{1}{209}-\frac{1}{209}\right)-\frac{1}{211}\)

\(=\frac{1}{11}-\frac{1}{211}=\frac{200}{2321}\)

~ Hok tốt ~

Answer 4

GIẢI:

\(\frac{2}{11.12}+\frac{2}{13.15}+...+\frac{2}{209.211}\)

\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{209}-\frac{1}{211}\)

\(=\frac{1}{11}-\frac{1}{211}\)

\(=\frac{200}{2321}\)

Học tốt!