M L Aggarwal Solutions for Chapter: Sequences and Series, Exercise 11: CHAPTER TEST

The sum of an infinite $G.P.$ is $2$ and the sum of $G.P.$ made from the cubes of this infinite $G.P.$ is $24$. Find the $G.P.$.

In an infinite geometric progression, the sum of first two terms is $6$ and every term is four times the sum of all the terms that follow it. Find the $G.P.$

In an infinite geometric progression, the sum of first two terms is $6$ and every term is four times the sum of all the terms that follow it. Find its sum to infinity.

Find the geometric mean of $0.7$and $0.007$, $x^{3}y$ and $x{y}^3$

If $a, b, c$ are in $A.P.$, $x$ is in $G.M.$between $a$ and $b$, $y$i s the $G.M.$ between $b$ and $c$, then show that $b^2$ is the $A.M.$ between $x^2$ and $y^2$

Sum to $n$ terms the series $1+5+14+30+55+\dots$

Sum to $n$ terms the series whose $n^{th}$ term is $\frac{1}{4n^2-1}$

Find the $n^{th}$ term and the sum of $n$ terms of the series $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots$