Embibe Experts Solutions for Chapter: Sequence and Series, Exercise 1: Exercise 1

The sum of series, $6+66+666+........$ upto $n$ term is -

The value of $x$ in $(-\pi ,\pi )$ which satisfies the equation $8^{1+\left|\cos x\right|+\left|{\cos }^{2}x\right|+|{\cos }^{3}x\mid +\dots \dots \infty }=4^3$ is -

Three numbers whose product is $512$ are in $G.P.$ If $8$ is added to the first and $6$ to the second, the number will be in $A.P.$ The numbers are -

If $a, b, c$ form a $G.P.$ with common ratio $r$ such that $0<r<1$, and if $a, \frac{3b}{2}, -4c$ form an $A.P.$, then $r$ is equal to -

Let $a, b, c, d$ and $e$ be distinct positive numbers. If $a, b, c$ and $\frac{1}{c}$, $\frac{1}{d}$, $\frac{1}{e}$ both are in $\mathrm{AP}$ and $b, c, d$ are in $\mathrm{GP}$, then

The series $\frac{2x}{x+3}+{\left(\frac{2x}{x+3}\right)}^2+{\left(\frac{2x}{x+3}\right)}^3+\dots \dots \infty$ will have a definite sum when -

If three distinct positive numbers $a, b$ and $c$ are in $\mathrm{AP}$ such that $abc=4$, then the value of $b$ is always

The coefficient of $x^{101}$ in the expansion of $(1-x)(1-2x)\left(1-2^{2}x\right)\dots \left(1-2^{101}x\right)$ is -