Prove that 1+x+x2+...xn=1−xn+11−x
and how to prove this implies that for |x|<1
1+x+x2+........=11−x
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 11−x−xn+11−x.
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