Question

Tính :

B= 1/2+1/6+1/12+1/20+1/30+....+1/9900

 

Answer 1

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

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

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

Answer 2

B = 1/1.2 + 1/2.3 + ......+ 1/99.100

B = 1 - 1/2 + 1/2 - 1/3 +..........+ 1/99 - 1/100

B = 1 - 1/100

B = 99/100 nhé!

Answer 3

B=\(\frac{99}{100}\)