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For each integer n 2 1, let P(n) be the following equation Xn+1 i=1 i 2i = n2n+2 +2. Note the left hand side
For each integer n 2 1, let P(n) be the following equation Xn+1 i=1 i 2i = n2n+2 +2. Note the left hand side of the equation is Xn+1 i=1 i-2 i = 12+2-2 2+3+2 3+ +n2 n+(n+1)2n+1. (a) Write P(1). Is P(1) true? (b) Use mathematical induction to prove that P(n) holds true for all integers n 2 1.
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Ans a To write out P1 we substitute n 1 into the equation P1 1 2 2 2 1 21 2 2 2 4 6 b To prove Pn by ...
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Discrete Mathematics and Its Applications
Authors: Kenneth H. Rosen
7th edition
0073383090, 978-0073383095
