Embibe Experts Solutions for Exercise 3: EXERCISE

If $b^2, a^2, c^2$ are in $\mathrm{A}.\mathrm{P}.,$ then $a+b, b+c, c+a$ will be in

If $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c},$ then $a,b,c$ are in

Let $a+b+c=10, a, b, c>0$, then the maximum value of $a^2 b^3 c^5$ is -

Let $2x+3y+4z=9, x, y, z>0$  then the maximum value of ${\left(1+x\right)}^2 {\left(2+y\right)}^3 {\left(4+z\right)}^4$ is -

The sum of $1+\frac{2}{5}+\frac{3}{5^2}+\frac{4}{5^3}+....$ up to $n$ terms is

$\frac{1^3+2^3+3^3+4^3+...{12}^3}{1^2+2^2+3^2+4^2+...{12}^2}=$

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

Find the sum of the series $\left(1+2\right)+\left(1+2+2^2\right)+\left(1+2+2^2+2^3\right)+...$ upto $n$ terms.