Limits of Functions: Quiz

Problem 5

Let C(n) be a function that adds the first n powers of 1/2: C(0) = (1/2)0 = 1, C(1) = (1/2)0 + (1/2)1 = 1 + 1/2 = 3/2, C(2) = (1/2)0 + (1/2)1 + (1/2)2 = 1 + 1/2 + 1/4 = 7/4, and so on.

  1. Find a formula for C(n).
  2. What is the limit of C(n) as n gets large?

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