pls i need solution plssss...asap n lim ∈ ((r^3 /(r^4 +n^4 ))) n→∞ r=1 please try and understand the way i typed it


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Question Number 65945 by Chi Mes Try last updated on 06/Aug/19

$p l s i n e e d s o l u t i o n p l s s s s . . . a s a p$ $n$ $l i m \in (\frac{r^{3}}{r^{4} + n^{4}})$ $n \to \infty r = 1$ $p l e a s e t r y a n d u n d e r s t a n d t h e w a y i t y p e d i t$
Commented by MJS last updated on 06/Aug/19

$\lim_{n \to \infty} \underset{r = 1}{\sum^{n}} \frac{r^{3}}{r^{4} + n^{4}}$ $is this what you mean ?$
Commented by mathmax by abdo last updated on 06/Aug/19

$l e t S_{n} = \sum_{k = 1}^{n} \frac{k^{3}}{n^{4} + k^{4}} \Rightarrow S_{n} = \sum_{k = 1}^{n} \frac{1}{n} \times \frac{{(\frac{k}{n})}^{3}}{1 + {(\frac{k}{n})}^{4}}$ $s o S_{n} i s R i e m a n s u m a n d {l i m}_{n \to + \infty} S_{n} = \int_{0}^{1} \frac{x^{3}}{1 + x^{4}} d x$ $= {[\frac{1}{4} l n (1 + x^{4})]}_{0}^{1} = \frac{l n (2)}{4}$
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