Monday, 15 June 2015

proof verification - prove that 1+x+x2+...xn=frac1xn+11x




Prove that 1+x+x2+...xn=1xn+11x



and how to prove this implies that for |x|<1



1+x+x2+........=11x



for the first part we can prove by induction but to get second one by using first one


Answer



Hint:




(Both for the induction part and for the limit).



Rewrite the r.h.s. as 11xxn+11x.


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