Prove each of the following statements using mathematical induction. (b) n Prove that for any positive integer n, Σj. 2³ = (n − 1)2n+¹ + 2 j=1 *Show All Your Work

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A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

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Q: a. Sketch the graph of r(t) = ti+t2j. Show that r(t) is a smooth vector-valued function but the…

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Q: Define P(n) to be the assertion that: n n j= j=1 = (a) Verify that P(3) is true. (b) Express P(k).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…