I'm so lost with this problem! Please help!!

Question

1/5+1/10+1/20+1/40+...
A- It diverges; it has a sum
B- It diverges; it does not have a sum
C- It converges; it has a sum
D- It converges; it does not have a sum.

I believe that it is answer choice d, not all quite sure though.

Answer 1

it's just a GP, with
a = 1/5
r = 1/2
So,
S = a/(1-r)

Answer 2

s = 1/5(1-1/2)

Answer 3

not quite.
But it does not matter what S is. It exists.

Answer 4

So it equals 2/5, i did the math. so it is c correct? Converges with a sum.

Answer 5

correct on both counts.

Answer 6

Thank you!

Answer 7

it is GP
s=a/(1-r)