Question

What is the sum of the infinite geometric series
1/2 +1/4 + 1/8 + 1/16 +... ?

Answer 1

well, you can see the pattern, right?

Answer 2

a1=1/a0, a2=1/2*a1, a3=1/2*a2, etc.

Answer 3

converges to 1

Answer 4

there is an exact formula but I don't remember sorry...

Answer 5

\[\sum_{n=0}^{\infty}\frac{ 1 }{ 2n }\]

Answer 6

I think that's about right.

Answer 7

it's geometric.

Answer 8

the formula is Sn=(t1(1-r^n))/1-r

Answer 9

Any infinite geometric series has an infinite sum of

S = a/(1-r)

where

a = first term
r = common ratio and |r| < 1


If |r| > 1, then the series doesn't converge

Answer 10

the formula for the sum uses a=first term r=ration you're multiplying by and the formula is a/(1-r) if I remember correctly

Answer 11

whats the n amount? in the formula i listed above?

Answer 12

the formula you listed sparky16 is only used for partial sums

Answer 13

oh is it this formula:
S=t1/1-r

and r has to be less than 1

Answer 14

more like |r|<1, but yes

Answer 15

so after plugging that in, I got 1.
Is that correct?

Answer 16

yes

S = a/(1-r)

S = (1/2)/(1-1/2)

S = (1/2)/(1/2)

S = 1

Answer 17

thank you so much(:

Answer 18

np