EXERCISE-1

The sum of $n$ terms of $1^2+\left(1^2+2^2\right)+\left(1^2+2^2+3^2\right) .....$  is-

$1.2^2+2.3^2+3.4^2+\dots \dots$ upto $n$ terms, is equal to-

The sum of $n$ terms of the series $\frac{\frac{1}{2}·\frac{2}{2}}{1^3}+\frac{\frac{2}{2}·\frac{3}{2}}{1^3+2^3}+\frac{\frac{3}{2}·\frac{4}{2}}{1^3+2^3+3^3}+\dots \dots$ is

$\frac{1^2}{1}+\frac{1^2+2^2}{1+2}+\frac{1^2+2^2+3^2}{1+2+3}+.....$ upto $n$ term is 

Sum of terms of the series $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\mathrm{......}$ is-

$\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....$ upto $n$ terms is-

The sum of the series $\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+\mathrm{.....}$ upto $n$ terms

$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\mathrm{.....}$ upto $n$ terms equal to-