Prove that there exists a real number $x$ for which $\displaystyle \sum_{k=0}^n a_kx^k = 0$
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
140437
If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$
324
Show uncountable set of real numbers has a point of accumulation
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
18093
Find $x$ such that $\sum_{k=1}^{2014} k^k \equiv x \pmod {10}$
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
130149
Computablility of a real number
76925
Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $
44706
Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$
125707
A simple proof (hopefully) for $2^x \neq 0$
90199
Prove that there exists a constant $c>0$ such that the following happens
93813
How to show that $\sum\limits_{k=0}^n (-1)^k\tfrac{{ {n}\choose{k}}}{{ {x+k}\choose{k}}} = \frac{x}{x+n}$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
138446
Proving that there exists an irrational number in between any given real numbers
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$