Vinod Singh and Shweta Pawar Solutions for Chapter: Sequence and Series, Exercise 1: Classical Thinking

For a natural number $n$, $\sum _{r=1}^n\left(2r+5\right)=$ 
 

If $1^2+2^2+3^2+\dots +n^2=1015$, then the value of $n$ is
 

The sum of $(31{)}^2+(32{)}^2+(33{)}^2+\dots .+(60{)}^2$ is
 

The sum of $n$ terms of the following series $1.2+2.3+3.4+4.5+\dots \dots ..$ will be
 

$2·1^2+3·2^2+4·3^2+\dots .$ upto $10$ terms$=$
 

If $y=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\dots .,$ then $x$ is equal to
 

The sum of the series $x^2+\frac{x^4}{2}+\frac{x^6}{3}+\frac{x^8}{4}+\dots .,\left|x\right|<1$, is
 

${\log }_{e}3-\frac{{\log }_{e}9}{2^2}+\frac{{\log }_{e}27}{3^2}-\frac{{\log }_{e}81}{4^2}+\dots$ is