Question

tính giá trị biểu thức \(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+.....+\dfrac{1}{9900}\)

Answer 1

A = \(\dfrac{1}{12}\)+ \(\dfrac{1}{20}\)+ \(\dfrac{1}{30}\)+...+\(\dfrac{1}{9900}\)

A = \(\dfrac{1}{3\times4}\)+ \(\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{99\times100}\)

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

A = \(\dfrac{1}{3}\) - \(\dfrac{1}{100}\)

A = \(\dfrac{97}{300}\) 

Answer 2

Lời giải:

Gọi tổng trên là $A$

$A=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{99.100}$

$=\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+...+\frac{100-99}{99.100}$

$=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{99}-\frac{1}{100}$

$=\frac{1}{3}-\frac{1}{100}=\frac{97}{300}$