## klimenkov 3 years ago 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.

1. klimenkov

Please, write a formula for $$S_n$$ and it's proof.

2. klimenkov

3. helder_edwin

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 $\large qS_n=b_1q+b_1q^2+\dots+b_1q^n$

4. experimentX

|dw:1349108015779:dw|

5. helder_edwin

from these $\large qS_n-S_n=b_1q^n-b_1$ and if $$q\neq1$$ $\large S_n=b_1\cdot\frac{q^n-1}{q-1}$

6. klimenkov

So, who owns a medal? Who was really the first? I think @helder_edwin.

7. helder_edwin

i don't think that matters.

8. helder_edwin

i think the point is that if u found the posts useful.

9. klimenkov