R D Sharma Solutions for Chapter: Some Special Series, Exercise 4: MULTIPLE CHOICE QUESTIONS (MCQs)

The sum to $n$ terms of the series $\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+\dots \dots$ is

The sum of the series : $\frac{1}{{\log }_{2}4}+\frac{1}{{\log }_{4}4}+\frac{1}{{\log }_{8}4}+\dots +\frac{1}{{\log }_{2^n}4}$ is

The value of $\sum _{r=1}^n\left\{\left(2r-1\right)a+\frac{1}{b^r}\right\}$ is equal to

If $\mathrm{\Sigma }n=210,$ then $\mathrm{\Sigma }{n}^2=$

If $S_n=\sum _{r=1}^n\frac{1+2+2^2+\dots \text{ Sum to }r\text{ terms }}{2^r},$ then $S_n$ is equal to

If $1+\frac{1+2}{2}+\frac{1+2+3}{3}+\dots$ to $n$ terms is $S$. Then $S$ is equal to

Sum of $n$ terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\dots .$ is

The sum of the series $\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+\frac{80}{81}+\dots$ to $n$ terms is