Question

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

Answer 1

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

Answer 2

Answer 3

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

= 1/1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100

= 1/1 - 1/100

= 99/100.

Answer 4

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

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

Answer 5

99/100