hey mate, here is your answer.

Answer:

Step-by-step explanation:

Since,k belongs to natural numbers,we can substitute k=1,2,3,...

Take k=1.

i^(4k+1)=i

i^(4k-1)=-i

for k=1

So,

{i-(-i)}/2=2i/2=I

Hence, value of the given expression is i