Asked by Topperlearning User | 30th Sep, 2016, 06:03: PM

Expert Answer:

A space G. P space w i t h space f i r s t space t e r m space a space a n d space c o m m o n space r a t i o space r space i s space g i v e n space b y space a comma a r comma a r squared comma....
W e space n e e d space t o space f i n d space S subscript n equals space a plus a r plus a r squared plus... plus a r space to the power of n minus 1 end exponent
space S subscript n left parenthesis a minus a r right parenthesis equals left parenthesis a minus a r right parenthesis left parenthesis a plus a r plus a r squared plus... plus a r space to the power of n minus 1 end exponent right parenthesis
space space space space space space space space space space space space space space space space space space space space equals left parenthesis a squared plus a squared r plus a squared r squared plus... plus a squared r to the power of n minus 1 end exponent right parenthesis minus left parenthesis a squared r plus a squared r squared plus... plus a squared r to the power of n right parenthesis
space space space space space space space space space space space space space space space space space space space space space equals a squared minus a squared r to the power of n
S subscript n equals fraction numerator a left parenthesis 1 minus r to the power of n right parenthesis over denominator 1 minus r end fraction
f o r space vertical line r vertical line less than 1 space a n d space n rightwards arrow infinity space r to the power of n rightwards arrow 0
s o space S subscript infinity equals a divided by left parenthesis 1 minus r right parenthesis

Answered by  | 30th Sep, 2016, 08:03: PM