Question

Derive the formula for the sum of a finite geometric series

Answer 1

$let \: the \: infinite \: gp \: \: be \: a \: a {r \: }^{2} \: a r{}^{3} ...$
where a is the first term of GP, and r be its common difference,

if |r| > 1
Sum of its infinite terms will be infinte.

if |r| < 1

$s \: = \frac{a(r {}^{n} - 1) }{r - 1}$
on n tending to infinte and |r| < 1 , r^n tends to 0
S = a(-1)/r-1

S = a/1-r

Hope you get it. :)