Question: Let us prove this formula: S= i=0 n b i = 1- b n+1 1-b Try this expression with b = 2 and n =

Let us prove this formula:

S=i=0nbi=1-bn+11-b

  1. Try this expression with b = 2 and n = 4. Find S using the two expressions (the sum and the fraction).
  2. Let us prove this expression using induction
    1. Show the base (basis) case
    2. Show the induction step by answering these questions:
      1. What is your hypothesis to use for the induction step?
      2. Now, complete the induction step

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