Criteria of a convergent geometric series?

Algebra Level 3

If the infinite series $x + x^2 + x^3 + \cdots$ equals 2017, can it be true that $x^{-1} + x^{-2} + x^{-3} + \cdots=2017?$

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1 solution

Sardor Yakupov
Jul 20, 2017

If $x+x^2+x^3+...$ equals to a finite number, than $\lim _{ n\rightarrow \infty }{ { x }^{ n }=0 }$ . So, |x| < 1. Than $\left| { x }^{ -n } \right| >1$ and this series diverges.

Criteria of a convergent geometric series?

1 solution

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