Question

1/2 +1/6 +1/12 +1/20 +1/30 +  +1/9702 +1/9900=T .Tim T

 

Answer 1

T=1/2+1/6+1/12+..............+1/9702+1/9900

T=1/1x2+1/2x3+1/3x4+...........+1/98x99+1/99x100

T=1-1/2+1/2-1/3+1/3-1/4+.........+1/98-1/99+1/99-1/100

T=1-1/100

T=99/100

           Vậy T=99/100

Answer 2

Giải :

Đặt : A = \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{9702}+\frac{1}{9900}\)

\(\Rightarrow A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{98.99}+\frac{1}{99.100}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

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

Answer 3

99/100 duyệt đi

Answer 4

Đặt Z = \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+......+\frac{1}{9702}+\frac{1}{9900}\)

\(\Rightarrow Z=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{98.99}+\frac{1}{99.100}\)

\(\Rightarrow Z=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

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

Answer 5

Ta có :

\(T=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9702}+\frac{1}{9900}\)

\(T=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(T=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

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

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