Question

A=1/2+1/6+1/12...........1/99.100
Ai nhanh mk sẽ tick nha(mk đng cần gấp)

 

Answer 1

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{99.100}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)