Question

a) 1/1x2 + 1/2x3 + 1/3x4 + ........ + 1/99x100.

b) 1/2 + 1/4 + 1/8 + ......... + 1/2016

                           

Answer 1

\(a,\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

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

\(b,\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2016}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...-\frac{1}{2016}\)

\(=1-\frac{1}{2016}=\frac{2015}{2016}\)

Answer 2

a)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/99-1/100)

=1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100

=1-1/100=99/100

Answer 3

b)=(1/1-1/2)+(1/2-1/4)+(1/4-1/8)....+(1/1008-1/2016)

=1-1/2+1/2-1/4+1/4-1/8+.....+1/1008-1/2016

=1-1/2016=2015/2016