if-a-and-b-are-positive-numbers-then-an-b-p-converges-if-p-gt-1-and-diverges-if-p-1-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 163396 by HongKing last updated on 06/Jan/22

if a and b are positive numbers then Σ (an + b)^(-p) converges if p>1 and diverges if p≤1

$$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\mathrm{then}\:\:\Sigma\:\left(\mathrm{an}\:+\:\mathrm{b}\right)^{-\boldsymbol{\mathrm{p}}} \:\:\mathrm{converges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}>\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{diverges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}\leqslant\mathrm{1} \\ $$

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if-a-and-b-are-positive-numbers-then-an-b-p-converges-if-p-gt-1-and-diverges-if-p-1-

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