Question

Tính nhanh tổng A

A = ​\(\frac{1}{5.6}\)+ \(\frac{1}{6.7}\)+ \(\frac{1}{7.8}\)+ ....... + \(\frac{1}{99.100}\)

Answer 1

\(a,\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{99.100}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{5}-\frac{1}{100}=\frac{20}{100}-\frac{1}{100}=\frac{19}{100}\)

Answer 2

Bài này bạn làm theo công thức:1/axa+1=1/a-1/a-1

Ta có:

A=1/5-1/6+1/6-1/7+1/7-1/8+...+1/99-1/100

A=1/5-1/100

A=19/100