If S is the sum to infinity of a G.P., whose | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(b) Let $r$ be the common ratio of the $G.P. $ Then

$S = \frac{a}{{1 - r}}$

$ \Rightarrow $$r = 1 - \frac{a}{S}$

Now ${S_n} = $ Sum of $n$ te

Vedclass · Accepted Answer

$S\left[ {1 - {{\left( {1 - \frac{a}{S}} \right)}^n}} \right]$

Vedclass · Answer

(b) Let $r$ be the common ratio of the $G.P. $ Then

$S = \frac{a}{{1 - r}}$

$ \Rightarrow $$r = 1 - \frac{a}{S}$

Now ${S_n} = $ Sum of $n$ terms

$ = a\left( {\frac{{1 - {r^n}}}{{1 - r}}} \right) = \frac{a}{{1 - r}}(1 - {r^n}) = S\left[ {1 - {{\left( {1 - \frac{a}{S}} \right)}^n}} \right]$.

If $S$ is the sum to infinity of a $G.P.$, whose first term is $a$, then the sum of the first $n$ terms is

Similar Questions

The sum can be found of a infinite $G.P.$ whose common ratio is $r$

The greatest integer less than or equal to the sum of first $100$ terms of the sequence $\frac{1}{3}, \frac{5}{9}, \frac{19}{27}, \frac{65}{81}, \ldots \ldots$ is equal to

If the first term of a $G.P.$ ${a_1},\;{a_2},\;{a_3},..........$ is unity such that $4{a_2} + 5{a_3}$ is least, then the common ratio of $G.P.$ is

The sum of the series $3 + 33 + 333 + ... + n$ terms is

The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is