Show that $(fg)^{(n)}(x)=\displaystyle\sum_{k=0}^n {n\choose k} f^{(n-k)}(x)g^{k}(x)$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
157426
Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$
48642
Let $f(n) = \sum_{(k,n)=1} e^\frac{2\pi ik}{n}$. Show that $f(n) = \sum_{k=1}^{n}\left(\sum_{d\mid (k,n)} \mu(d)e^{\frac{2\pi ik}{n}} \right) $
26446
Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
140614
Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
15943
show $\sum_{cyc}(1-x)^2\ge \sum_{cyc}\frac{z^2(1-x^2)(1-y^2)}{(xy+z)^2}.$
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
83036
f(g(x)) has a degree divisible by n
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
123967
Proof of a generating functions formula
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
925
Prove that $F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$ where $F(n)$ is the $n$-th fibonacci number
117770
Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$