Question

[LuuHieu1107]

Tính:
B=1/1.2.3+1/2.3.4+1/3.4.5+............+1/98.99.100

Answer 1

[Thắng Nguyễn]

B=1/1.2.3+1/2.3.4+1/3.4.5+............+1/98.99.100

 \(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)\)

\(=\frac{1}{2}\cdot\frac{4949}{9900}\)

\(=\frac{4949}{19800}\)

Answer 2

[soyeon_Tiểu bàng giải]

\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)

\(B=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)

\(B=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(B=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{9900}\right)\)

\(B=\frac{1}{2}.\frac{4949}{9900}=\frac{4949}{19800}\)