Question

3/2+ 7/6 + 13/12 + 21/20 +31/30 + 42/41+ 57/56+ 73/71+ 91/90. mọi ng cho mình lời giải chi tiết vs ạ.

 

Answer 1

A=1+1/2+1+1/6+1+1/12+...+1+1/90=

=9+1/2+1/6+1/12+...+1/90

1/2+1/6+1/12+...+1/90=

1/1x2+1/2x3+2/3x4+...+1/9x10=

\(=\dfrac{2-1}{1x2}+\dfrac{3-2}{2x3}+\dfrac{4-3}{3x4}+...+\dfrac{10-9}{9x10}=\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}=\)

\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)

\(\Rightarrow A=9+\dfrac{9}{10}=9\dfrac{9}{10}\)