Amit M Agarwal Solutions for Chapter: Sequence and Series, Exercise 3: Work Book Exercise 3.3

If $a, b, c$ and $d$ are distinct positive real numbers in $\mathrm{HP}$, then

The $4th$ term of the sequence $3,\frac{3}{2},1,...$ is

If $\left|x\right|<1,$ then $1+3x+5x^2+7x^3+\dots$ is equal to

The sum of $n$ terms of the series $1+2\left(1+\frac{1}{n}\right)+3{\left(1+\frac{1}{n}\right)}^2+\dots$ is

If$a, b, c, d$ and $p$ are distinct real numbers such that $\left(a^2+b^2+c^2\right)p^2-2\left(ab+bc+cd\right)$ $p+\left(b^2+c^2+d^2\right)\le 0,$ then $a, b, c$ and $d$ are in

If$x, y, z$ and $w$ are non-zero real numbers such that $\left(x^2+y^2+z^2\right)\left(y^2+z^2+w^2\right)\le {\left(xy+yz+zw\right)}^2$, then $x, y, z$ and $w$ are in

If $0\le \theta <\frac{\pi }{2},$ then $\cos \theta +\sec \theta$ is

The least value of the expression $5^{\sin x-1}+5^{-\sin x-1}$ is