Sunday, 8 June 2014

sequences and series - Proof by Induction sumk1i=02i=2k1





Prove mathematical induction k1i=02i=2k1


Answer



Assuming you mean 2k1 then



base case k=1 then



11i=02i=1=211



Now
ki=02i=k1i=02i+2k=2k1+2kassuming k1i=1=2k1=212k1=2k+11



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