\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)
\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+...+\frac{1}{98.99}-\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{9900}=\frac{4950}{9900}-\frac{1}{9900}=\frac{4949}{9900}\)
Ta có:
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)
\(\Rightarrow\frac{1}{2}A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+....+\frac{2}{98.99.100}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+....+\frac{1}{98.99}-\frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{1.2}-\frac{1}{99.100}\)
\(\Rightarrow A=\frac{4949}{9900}.\frac{1}{2}=\frac{4949}{19800}\)
A= 1/1.2.3+1/2.3.4+1/3.4.5+...+1/98.99.100
A=1/1.2-1/2.3+1/2.3-1/3.4+1/3.4+...+1/98.99-1/99.100
A= 1/1.2 +(1/2.3-1/2.3)+(1/3.4-1/3.4)+...+(1/98.99+1/98.99)+1/99.100
A= 1/1.2 +0+0+0+...+0+1/99.100
A= 1/2+1/9900
A=4950/9900+ 1/9900
A= 4951/9900
Câu trả loi của bn giống mk quá,cảm ơn bn nha.
