Prove mathematical induction k−1∑i=02i=2k−1
Answer
Assuming you mean 2k−1 then
base case k=1 then
1−1∑i=02i=1=21−1
Now
k∑i=02i=k−1∑i=02i+2k=2k−1+2kassuming k−1∑i=1=2k−1=212k−1=2k+1−1
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