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1d
comment How to solve $\sum_{k=1}^n\frac{k}{n^2+k}$?
$k=n^2-n^2+k = n^2+k-n^2$
1d
answered How to solve $\sum_{k=1}^n\frac{k}{n^2+k}$?
Aug
28
awarded  Yearling
Aug
27
answered Limits using definite integration
Aug
22
comment Does writing $f(x)\sim \ell$ have a sense?
could the downvoter please explain?
Aug
21
answered Does writing $f(x)\sim \ell$ have a sense?
Aug
20
comment Combinations with repetition with limits.
Use multinomial identity
Aug
20
comment Combinations with repetition with limits.
'10 sets 2 cards each'= 20 cards
Aug
19
answered Combinations with repetition with limits.
Aug
16
comment Prove that $\sum\frac{n+1}{(n+2)n!}$ converges
$n+1<n+2$ and convergence comes out immediately due to Maclaurin series of $e^x$
Aug
12
answered Prove that $\lim_{n\longrightarrow \infty}\frac{5}{n^3}=0$
Aug
9
answered Limit of $\sqrt[2n+1]{n^2+n}$
Aug
9
comment Prove that $\limsup_{n \rightarrow \infty} (f_n(x))^{1/n} \leq1 $
Thanks, so the support is $[0,\frac{1}{n}]$. I guess I missed it.
Aug
8
comment Prove that $\limsup_{n \rightarrow \infty} (f_n(x))^{1/n} \leq1 $
I probably miss something, but it's it enough to notice that $f_n<\alpha <1$ due to the integral value for some constant $\alpha$, and hence the limit is 1.
Aug
8
comment Limits - What to do with the numerator?
wolframalpha.com/input/?i=plot%28x%2F%28-x%5E2%2B2%2Bx%29%29
Aug
8
comment Limits - What to do with the numerator?
you can't just 'ignore the signs': unlike the $\frac{1}{\infty}$ situation infinity has signs
Aug
8
answered Limit of $n!/n^n$ as $n$ tends to infinity
Aug
6
answered Squeeze Theorem for $ \lim_{n\rightarrow \infty }(3^n+1)^\frac{1}{n} $
Aug
4
comment $e\cdot(m(m-1)+1)\cdot k\cdot ( 1-\frac{1}{k})^m\leq 1$
the equality is wrong
Jul
9
revised How Independence and Mutually Exclusive connected?
deleted 8 characters in body