Subject Experts Solutions for Chapter: Sequence and Series, Exercise 1: PRACTICE EXERCISE

The sum of an infinite G.P. is $x$ and the common ratio $r$ is such that $\left|r\right|<1$. If the first term of the G.P. is $2$, then which one of the following is correct?

The sum of the series formed by the sequence $3, \sqrt{3}, 1, \dots$ upto infinity is

If ${\log }_{10}2, {\log }_{10}\left(2^x-1\right)$ and ${\log }_{10}\left(2^x+3\right)$ are three consecutive terms of an A.P., then the value of $x$ is

What is the sum of the series $0.5+0.55+0.555+\dots +n$ terms? 

The value of the infinite product $6^{\frac{1}{2}}\times 6^{\frac{1}{2}}\times 6^{\frac{3}{8}}\times 6^{\frac{1}{4}}\times \dots$ is

If the $nth$ term of an $\mathrm{AP}$ is $\frac{3+n}{4}$, then the sum of first $105$ terms is

What is the sum of $n$ terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\cdots$?

If $p, q, r$ are in one geometric progression and $a, b, c$ are in another geometric progression, then $ap, bq, cr$ are in