klimenkov
  • klimenkov
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.
Mathematics
katieb
  • katieb
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klimenkov
  • klimenkov
Please, write a formula for \(S_n\) and it's proof.
klimenkov
  • klimenkov
It is better, you don't use any sourses to help yourself.
helder_edwin
  • 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 \[ \large qS_n=b_1q+b_1q^2+\dots+b_1q^n \]

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experimentX
  • experimentX
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helder_edwin
  • helder_edwin
from these \[ \large qS_n-S_n=b_1q^n-b_1 \] and if \(q\neq1\) \[ \large S_n=b_1\cdot\frac{q^n-1}{q-1} \]
klimenkov
  • klimenkov
So, who owns a medal? Who was really the first? I think @helder_edwin.
helder_edwin
  • helder_edwin
i don't think that matters.
helder_edwin
  • helder_edwin
i think the point is that if u found the posts useful.
klimenkov
  • klimenkov
Yes, you are right. Hope @experimentX won't be sad about this.
experimentX
  • experimentX
doesn't matter much to me

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