# Proofs: conjecture and induction

**Question description**

let Sn= 1 + 2 + 2^2 + 2^3 +...+ 2^n-1

a) compute s1, s2, s3, s4, s5 and s6

b) conjecture a closed formula for Sn as a function of n

c) prove your conjecture by mathematical induction

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