Question

1. tính tổng A= 1/(1*2*3)+ 1(2*3*4) +1/(3*4*5) +........+ 1(98*99*100)
 

Answer 1

\(A=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{98\cdot99\cdot100}\)

\(A=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{99\cdot100}\right)\)

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

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

\(A=\frac{1}{9898}\)