Question

\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{99\times100}\)

Answer 1

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

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

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

Answer 2

Answer 3

​Di hoc duong pha do cua co

Answer 4

1/1x2+1/2x3+...+1/99x100

=1-1/2+1/2-1/3+...+1/99-1/100(gạch cách số đối nhau đi)

=1-1/100=99/100