Well first of this cant be an infinite series since the sum is divergent. And also the equations presented before are somewhat difficult to work with when dealing with a sum.
Code:
n
Sum -((-4)^k)/20
k=1
Then the sum just becomes
Code:
remember: a1*(1-r^n)/(1-r) ; where r is -4 and a1 is the first term .2
so:
(1-Tn)/25 ; Where Tn is the finishing term of your sum