Question

Prove for a medal.
The sum of the first \(n\) terms of the geometric sequence \(S_n\).
\(b_1\) is the first term, \(q\) is the ratio.

Answer 1

Please, write a formula for \(S_n\) and it's proof.

Answer 2

It is better, you don't use any sourses to help yourself.

Answer 3

if \(b_n=b_1q^{n-1}\). Let
\[ \large S_n=b_1+b_2++b_3\dots+b_n=b_1+b_1q+b_1q^2+\dots+b_1q^{n-1} \]
then
\[ \large qS_n=b_1q+b_1q^2+\dots+b_1q^n \]