Show that $3^n = 2^{O(n)}$
113159
Big O/little o true/false
136574
Show $g^{(n)}(0)=0$ for all $n$
8609
Prove by induction that $n!>2^n$
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
48053
Show that 13 divides $2^{70}+3^{70}$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
100361
Show that ord$_{p}2 = 2^{n + 1}$.
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
60041
Number of real roots of $3^x+4^x=2^x+5^x$ with proof
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
77579
Proof by induction that $ 169 \mid 3^{3n+3}-26n-27$
115204
Show that SO(n) is a normal subgroup of O(n)
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
86479
How to Prove with Mathematical Induction $3^n > n^2$