Is the series sum from n=1 to infinity of (-1)^n convergent or divergent? Justify your answer. Can you now resolve the difficulty of the following:Divergent series:
S=1+1/2+1/4+1/8+1/16+…You have probably seen the following trick to sum this series: if we call the above sum S, then if we multiply by 2, we obtain: 2S=2+1+1/2+1/4+…=2+SHence S=2, so the series sumes to 2. However, if you apply the same trick to the series S=1+2+4+8+16+… one gets nonsensical results:
2s=2+4+8+16+…=S-1 => S=-1So the same reasoning that shows that 1+1/2+1/4+…=2 also gives that 1+2+4+8+…=-1. Why is it that we trust the first equation but not the second? A similar example arises with the series:
S=1-1+1-1+1-1+…;We can write S=1-(1-1+1-1+…)=1-S and that S=1/2
Instead, we can write S= (1-1)+(1-1)+(1-1)+…=0+0+… and hence S=0
Or, we can write S=1+(-1+1)+(-1+1)+…=1+0+0+…and S=1. Which one is correct?I used LaTeX to generate a PDF file for the solution.

Why Choose Us

  • 100% non-plagiarized Papers
  • 24/7 /365 Service Available
  • Affordable Prices
  • Any Paper, Urgency, and Subject
  • Will complete your papers in 6 hours
  • On-time Delivery
  • Money-back and Privacy guarantees
  • Unlimited Amendments upon request
  • Satisfaction guarantee

How it Works

  • Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
  • Fill in your paper’s requirements in the "PAPER DETAILS" section.
  • Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
  • Click “CREATE ACCOUNT & SIGN IN” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page.
  • From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.