Determine-whether-the-series-U-n-1-2n-2-1-n-2-is-convergent-or-not-M-m-

Question Number 185470 by Mastermind last updated on 22/Jan/23

Determine whether the series

U_{n} = \frac{1 + {2 n}^{2}}{1 + n^{2}} is convergent or not

M . m

Commented by mr W last updated on 22/Jan/23

U_{n} = 2 - \frac{1}{1 + n^{2}}

t h e r e s t y o u s h o u l d k n o w .

Commented by Mastermind last updated on 22/Jan/23

I think the series is divergent simply

because A series cannot be convergent

unless it is ultimately tends to zero

Double subscripts: use braces to clarify

and is not equals zero

Commented by Frix last updated on 23/Jan/23

Is U_{n} = \frac{1 + 2 n^{2}}{1 + n^{2}} a sequence (or progression)

and the series {we}^{'} re talking about is

S_{n} = \underset{k = 0}{\sum^{n}} U_{k} or is U_{n} = \underset{k = 0}{\sum^{n}} a_{k} = \frac{1 + 2 n^{2}}{1 + n^{2}} and we

{don}^{'} t know (and {don}^{'} t need) a_{n} ?

In the 1^{st} case S_{\infty} = + \infty (divergent), in the

2^{nd} case U_{\infty} = \underset{k = 0}{\sum^{\infty}} a_{k} = 2 (convergent) .

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