Concept explainers
Exercises 49-51 present incorrect proofs using mathematical induction. You rill need toidentify"anerror in reasoningin each exercise.
50. Whatisrangivith this "proof?
Tk™7or every posihVeintegerrc,l^i*(b+W/2.
Basis 5tep: The formula is true for re =1.
kkitkiStep: Suppose that £._,/ = [«+ !.'¦'/. Then [_'.; = (£., 0+^1+1). By the inductive hypothesis, we have 2J1l1l(»(n+-)!/2+ji+I¦ (n!+n+j)/: + h + I = (r + .In +])P. =(n+|):/2=[(ji+l)+!l'7:,complen,ngtheinducn,vestep.
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