# sequence converge, finding its limit.

• Oct 7th 2010, 02:52 PM
jax
sequence converge, finding its limit.
Hello,
I was wondering if this sequence converges, and if it does what is the limit?

(a_n), where a_n=(1)+(1/2)+(1/2^2)+(1/2^3)+...+(1/2^n).

p.s- I know that the sequence a_n=(1/2,1/4,1/6...) its limit is zero, but I'm not really sure about the sequence above.

Thanks!!
• Oct 7th 2010, 03:01 PM
Quote:

Originally Posted by jax
Hello,
I was wondering if this sequence converges, and if it does what is the limit?

(a_n), where a_n=(1)+(1/2)+(1/2^2)+(1/2^3)+...+(1/2^n).

p.s- I know that the sequence a_n=(1/2,1/4,1/6...) its limit is zero, but I'm not really sure about the sequence above.

Thanks!!

I guess you mean "series", the sum of the terms of the sequence,
and you want to know if this sum converges as n goes to infinity.

So your $a_n$ should be $S_n$

This is a geometric series, 1st term 1 and common ratio 0.5

Hence it's sum for n terms is $\displaystyle\frac{1-r^n}{1-r}$

and as n goes to infinity, the numerator goes to 1, while the denominator is 0.5.

So the sum converges.
• Oct 7th 2010, 03:01 PM
Also sprach Zarathustra
Hint: Find formula for a_n... (geometric series).