Question

A = 1/1.3 +1/3.5 + 1/5.7 + ... +1/199.201

Answer 1

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{199.201}\).

\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{199.201}\)

\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{199}-\frac{1}{201}\)

\(2A=\frac{1}{1}-\frac{1}{201}\)

\(2A=\frac{201-1}{201}\)

\(2A=\frac{200}{201}\)

\(A=\frac{200}{201}:2\)

\(A=\frac{200}{402}\)

Answer 2

Đáp số là 100/201

Answer 3

hông biết đúng không nữa?

Answer 4

A = \(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{199.201}\)

= \(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{199}-\frac{1}{201}\right)\)

= \(\frac{1}{2}\left(1-\frac{1}{201}\right)\)

= \(\frac{1}{2}.\frac{200}{201}\)

= \(\frac{100}{201}\)