Question

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

• A. S
• B. S $\left[ 1 - \left( 1 - \frac { \mathrm { a } } { \mathrm { S } } \right) ^ { \mathrm { n } } \right]$
• C. a $\left[ 1 - \left( 1 - \frac { \mathrm { a } } { \mathrm { S } } \right) ^ { \mathrm { n } } \right]$
• D. None of these

Answer 1

Answer: (B)

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

Answer 2

Let r be the common ratio of the G.P. then

S = Ž r = 1 – $\frac { \mathrm { a } } { \mathrm { s } }$

Now S_n = sum of n terms

= a = $\frac { a } { 1 - r }$ (1 – rⁿ) = S