If n is a positive integer then prove that `(1+i)^(n)+ (1-i)^(n)= (sqrt2)^(n+2) cos ((n pi)/(4))`

Prove that ((n+1)/(2))^(n) gt (n!)

If n is a positive integer then 5^(2n+2)-24n-25 is divisible by

Which one of the following is true? a) (1+(1)/(n))^(n)ltn^(2),n is a positive integer b) (1+(1)/(n))^(n)lt2,n is a positive integer c) (1+(1)/(n))^(n)ltn^(3),n is a positive integer d) (1+(1)/(n))^(n)ge2,n is a positive integer

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2 tan^(-1)x^n

For positive integers n_(1), n_(2) the value of the expression (1+i)^(n_(1)) + (1+ i^(3))^(n_(1)) + (1+ i^(5))^(n_(2)) + (1+ i^(7))^(n_(2)) , where i= sqrt-1 is a real number if and only if