$n$-th power of a matrix
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
112084
Proof of a formula for the power set of a union of two sets
1409
Proving that the given set has at most $2^{n-1}$ elements
131708
Sum of powers of natural numbers
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
116823
VERIFYING: Proving an $n \times n$ Matrix Vector Space
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
51694
Radius of convergence of a power series with $a_n$ convergent
66499
Finding a 2x2 Matrix raised to the power of 1000
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
60416
Finding a permutation, and number of, from powers of the permutation
85237
Markov Chain - method of generating function -to find nth power
54369
Proof of $n^2 \leq 2^n$.
78298
On the nilpotence of the matrix $AB-BA$
36639
Prove by induction that $\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$