Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'am having problems solving this question and would just like a hint on how to go about solving it because I have gotten no where.

The question goes like this: Using the steps below, show that the following sequence converges: $$1+ 1/2 - 2/3 + 1/4 + 1/5- 2/6 + 1/7 + 1/8 - 2/9 + 1/10 + 1/11 - 2/12++-++-...$$

Consider the subsequence (s2, s3, s5, s6, s8, s9, ...) of the sequence of partial sums. Show that this is the sequence of partial sums of a related convergent series.

Thanks

share|improve this question
    
Compute s2, s3, s5, s6, s8, s9. Do you see a pattern? –  mathematician Jan 20 at 19:56
add comment

1 Answer 1

$$\frac1{3n+1}+\frac1{3n+2}-\frac2{3n+3}=\frac2{(3n+1)(3n+3)}+\frac1{(3n+2)(3n+3)}\sim\frac1{3n^2}$$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.