Answer to Question #42505 in Calculus for shasha

Question

Write the sum using summation notation, assuming the suggested pattern continues.

5 - 15 + 45 - 135 + ...

summation of five times threee to the power of the quantity n plus one from n equals zero to infinity

summation of five times negative three to the power of n from n equals zero to infinity

summation of five times thee to the power of n from n equals zero to infinity

summation of five times negative three to the power of the quantity n plus one from n equals zero to infinity

help me please and show work and explanatio

Answer 1

As we can see -15 = 5 * (-3); 45 = - 15 * (-3) and so on. This means that a_n = -3 * a_(n-1). The first term in our series is 5 so we obtain
5 - 15 + 45 - 135 + ... = summation from n equals zero to infinity of 5 * (-3)^n. (the second answer)