anonymous
  • anonymous
Determine the radius of convergence, the interval of convergence, and the sum of the series: summation from k=2 to infinite of k(x-2)^(k+1)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Apply the Ratio test. a(n+1) /a(n) = (k+1)(x-2)^(k+2) / k (x-2)^(k+1) = (k+1)/k (x-2) The series converges if | (k+1) / k (x-2) | < 1 lim k-->infinity (k+1)/k = 1 |x-2| < 1 Therefore the radius of convergence is 1 Therefore, the series converges if | x-2 | < 1 That is : -1 < x-2 < 1 add 2 throughout: 1 < x < 3 (1,3) is the interval of convergence.
anonymous
  • anonymous
Thank you! do you know about the sum?
anonymous
  • anonymous
sum of series is -(x-4)(x-2)^2 / (x-3)^2

Looking for something else?

Not the answer you are looking for? Search for more explanations.