Question

A=1/2! +2/3! +3/4!+...+9/10!

Chứng minh A<1.

mik cần gấp mấy bạn giúp mình nha.

Answer 1

\(A=\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{9}{10!}\)

\(A=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{4!}+...+\frac{10-1}{10!}\)

\(A=\frac{2}{2!}-\frac{1}{2!}+\frac{3}{3!}-\frac{1}{3!}+...+\frac{10}{10!}-\frac{1}{10!}\)

\(A=\frac{1}{1!}-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}+...+\frac{1}{9!}-\frac{1}{10!}\)

\(A=1-\frac{1}{10!}\)

\(\Rightarrow A< 1\left(đpcm\right)\)