SOLUTION: Prove by mathematical induction: ∑_(i=1)^n (3^i= 3(3^n-1)/2)

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Question 267871: Prove by mathematical induction: ∑_(i=1)^n (3^i= 3(3^n-1)/2)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

sum%283%5Ei%2Ci=1%2Cn%29+=+3%283%5En-1%29%2F2%29%0D%0A%0D%0A

It's true for n=1, because:




Assume true for any k such that 1%3C=n%3C=k

We want to prove that

sum%283%5Ei%2Ci=1%2Ck%2B1%29+=+3%283%5E%28k%2B1%29-1%29%2F2%29

Write that as the sum to k (for which we assume the formula holds,
plus the (k+1)st term or 3%5E%28k%2B1%29

 

Edwin