Show that $P_n=p(1-P_{n-1})+(1-p)P_{n-1}$ $n \ge 1$
114790
probability that a random variable is even
154945
$|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$
83407
How to show that that $q \mid p-1$?
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
121279
Proving an Combination formula $ \binom{n}{k} = \binom{n-1}{k}+\binom{n-1}{k-1}$
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
109778
Proving $(x-c)|(p(x)-p(c))$
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
103854
Showing that $Q_n=D_n+D_{n-1}$