Time remaining:
If the upper limit of a summation is infinite, does it even have a sum?

Algebra
Tutor: None Selected Time limit: 1 Day

I've been given a series in summation notation. The lower limit is n=1 and the limit above the sigma is infinity. I'm asked to write the first four terms and if the series diverges or converges (and I understand those parts). But then it asks me for the to find the sum of the series. How can it have a sum if it goes on infinitely?

Apr 12th, 2015

For a series ∑n=1 an consider the sequence of its partial sums s1 = a1, s2 = a1 +a2, s3 = a1 + a2 + a3, ... ,

sn = ∑k=1n ak , … . The series converges if and only if the sequence sn converges and the sum of the series is the limit of the sequence sn.

Example. The series ∑n=1 (1/2)n converges and its sum is 1 because sn = ∑k=1n (1/2)k = 1/2 + 1/4 + 1/8 + ... +(1/2)n = 1 – (1/2)n → 1 as n → ∞.


Apr 12th, 2015

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Apr 12th, 2015
...
Apr 12th, 2015
Dec 8th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer