by mathematical induction prove that : x2n-1 -1 is divisible by x-1 Share with your friends Share 9 Rishabh Mittal answered this To Prove:-x2n-1-1 is divisible by x-1.For n=1x21-1-1=x-1, divisible by x-1.So, it is true for n=1Let us assume that , it is true for n=k.x2k-1-1=x-1d, where d is any natural number.For n=k+1x2k+1-1-1=x2k-1.x2-1=x2x2k-1-1+1-1=x2x-1d+1-1=x2 x-1 d +x2-1=x2 x-1 d +x-1x+1=x-1x2d+x+1=x-1m, where m = x2d+x+1So, it is divisible by x-1 , for n=k+1.Hence by PMI , it is true for all n∈N. 21 View Full Answer
