Show that the sum `(1 + i^(2) + i^(4)+....+i^(2n))` is 0 when n is odd and 1 when n is even.

the sum (1 + i^(2) + i^(4)+....+i^(2n)) is , when n is odd

1 + i^(2n) + i^(4n) + i^(6n)

Show that sum_(n=1)^(25) (i^(n) + i^(n +1)) = i-1

The sum of first n terms of the series 1^(2)+ 2 . 2^(2) + 3^(2) + 2. 4 ^(2) + 5^(2) +… is n/2 (n+1) ^(2) when n is even , When n is odd then the sum will be-

Show that the function f:N rarr Z, defined by f(n)=(1)/(2)(n-1) when n is odd ;-1/2 n when n is even is both one-one and onto

The function f:NrarrZ defined by f(n)=(n-1)/(2) when n is odd and f(n)=(-n)/(2) when n is even, is

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even

Find the sequence of the numbers defined by a_n={1/n , when n is odd -1/n , when n is even