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1 a) Observe that 1+2 = 3 = 2^2-1, 1+2+2^2= 7 = 2^3-1, 1+2+2^2+2^3 = 15...

1 a) Observe that 1+2 = 3 = 2^2-1, 1+2+2^2= 7 = 2^3-1, 1+2+2^2+2^3 = 15 = 2^4−1, so it appears to be the case that 1+2+2^2+2^3+···+2n = 2n+1 − 1 for any integer n ≥ 0. Use induction on n to prove that this is true.

b) Find all three solutions of the equation 2z^3 + 4z^2 − z − 5 = 0.
(First try a few “simple” values of z)
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