Embibe Experts Solutions for Chapter: Sequence and Series, Exercise 1: CG PET 2019

If $G$ is the geometric mean of $x$ and $y$, then $\frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}$ will be

Arithmetic mean of two numbers is $6$ more than the geometric mean of the numbers. The ratio of numbers is $9:1$, then numbers are

If $a,b,c$ are in arithmetic progression, then $\frac{a}{bc},\frac{1}{c},\frac{2}{b}$ will be in

If $a>1,b>1$ and $c>1$ are in geometric progression, then $\frac{1}{1+{\log }_{e}a},\frac{1}{1+{\log }_{e}b},\frac{1}{1+{\log }_{e}c}$ will be in

The value of $\frac{2}{1}·\frac{1}{3}+\frac{3}{2}·\frac{1}{9}+\frac{4}{3}·\frac{1}{27}+\frac{5}{4}·\frac{1}{81}+...\infty$ is