R D Sharma Solutions for Chapter: Some Special Series, Exercise 2: EXERCISE 21.2

If the sum of $1+3+7+13+21+\dots$ to $n$ terms is $n\left(\frac{n^2+a}{b}\right)$ then find $a+b$.

If Sum the following series $3+7+14+24+37+\dots$ to $n$ terms is $\frac{kn}{a}\left[b{n}^2+cn+d\right]$, then $k+a+b+c+d=$

Sum the following series to $n$ terms:

$1+3+6+10+15+\dots$

If the sum of $1+4+13+40+121+\dots$ to $n$ terms is $\left(\frac{k^{n+1}-k-2n}{4}\right)$ then find the value of $k$.

If the sum of the series $4+6+9+13+18+\dots$ to $n$ terms is $\frac{n}{6}\left(a{n}^2+bn+c\right)$ then find the value of $a+b+c$.

If the sum of the series $2+4+7+11+16+\dots$ to $n$ terms is $\frac{n}{6}\left(a{n}^2+bn+c\right)$ then find the value of $a+b+c$.

Sum the following series to $n$ terms:

$\frac{1}{1.4}+\frac{1}{47}+\frac{1}{7.10}+\dots$

Sum the following series to $n$ terms:

$\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+\dots +\frac{1}{(5n-4)(5n+1)}$