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 2 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.
 2 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.

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klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0Please, write a formula for \(S_n\) and it's proof.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0It is better, you don't use any sourses to help yourself.

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.2if \(b_n=b_1q^{n1}\). Let \[ \large S_n=b_1+b_2++b_3\dots+b_n=b_1+b_1q+b_1q^2+\dots+b_1q^{n1} \] then \[ \large qS_n=b_1q+b_1q^2+\dots+b_1q^n \]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1349108015779:dw

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.2from these \[ \large qS_nS_n=b_1q^nb_1 \] and if \(q\neq1\) \[ \large S_n=b_1\cdot\frac{q^n1}{q1} \]

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0So, who owns a medal? Who was really the first? I think @helder_edwin.

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.2i don't think that matters.

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.2i think the point is that if u found the posts useful.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, you are right. Hope @experimentX won't be sad about this.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1doesn't matter much to me
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