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Question Number 119636 by I want to learn more last updated on 25/Oct/20

$$\mathrm{Test}\mathrm{wheather}\mathrm{convergent}$$$$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{3\mathrm{n}-1}{7^{\mathrm{n}}+2\mathrm{n}}$$

Answered by 1549442205PVT last updated on 26/Oct/20

$$\mathrm{Applying}{\mathrm{Cauchy}}^{\prime }\mathrm{s}\mathrm{sign}\mathrm{for}{\mathrm{u}}_{\mathrm{n}}=\frac{3\mathrm{n}-1}{7^{\mathrm{n}}+2\mathrm{n}}$$$$\underset{\mathrm{n}-\to \mathrm{\infty }}{\lim }{}^{\mathrm{n}}\sqrt{{\mathrm{u}}_{\mathrm{n}}}=\underset{\mathrm{n}\to \mathrm{\infty }}{\mathrm{Lim}}{}^{\mathrm{n}}\sqrt{\frac{3\mathrm{n}-1}{7^{\mathrm{n}}+2\mathrm{n}}}=$$$$=\frac{1}{7}<1\Rightarrow \mathrm{series}\mathrm{is}\mathrm{converge}$$

Commented by I want to learn more last updated on 27/Oct/20

$$\mathrm{Thanks}\mathrm{sir}$$

Commented by 1549442205PVT last updated on 27/Oct/20

$$\mathrm{You}\mathrm{are}\mathrm{welcome}.$$

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