Question

Does the series converge or diverge? If it converges, what is the sum?
infinity to n-1
-4(-1/2)^n-1

Answer 1

I know it converges.

Answer 2

Do you know how to write the first four terms?

Answer 3

No.. not sure

Answer 4

this is a geometric series with |r| < 1, so it converges

you don't even have to write out the first terms if you don't want to

Answer 5

yes, but how do I calculate the answer?

Answer 6

Oh, right, it's asking for the sum, too

the sum of a geometric sequence is S = a1/(1-r) where a1 is the first term and r is the common ratio

Answer 7

8/3?

Answer 8

I still don't completely understand. Sorry.

Answer 9

not quite, r = -1/2

Answer 10

a1 = -4(1/2)^0 = -4

Answer 11

Oh!! I think I get it now.

Answer 12

is it because it has 1/2 in the equation?

Answer 13

well, sort of

the general form of a geometric sequence is a1(r)^(n-1), so, yes, r = -1/2