If `A=d i ag(abc),` show that `A^n=d i ag(a^nb^nc^n)` for all positive integer `ndot`

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n .

Prove that quad 2^(n)>n for all positive integers n.

If A=[1101], prove that A^(n)=[1n01] for all positive integers n.

(-i)^(4n+3), where n Is a positive integer.

Using mathematical induction prove that (d)/(dx)(x^(n))=nx^(n-1) for all positive integers n.

Show that (-sqrt(-1))^(4n+3) =i , where n is a positive integer.

Show that (1-i)^(n)(1-(1)/(i))^(n)=2^(n) for all n in N

If A is a nilpotent matrix of index 2, then for any positive integer n,A(I+A)^(n) is equal to A^(-1) b.A c.A^(n) d.I_(n)

((1+i)/(1-i))^(4n+1) where n is a positive integer.

Show that the expression (n^5)/(5) + (n^3)/(3) + (7n)/(15) is a positive integer for all n in N .