SOLUTION: Prove the following using mathematical induction. Be sure to show the anchor as well as the full induction steps. Please show all the parts to the proof. 3+7+11+...+(4n-1)=n(2n+

Question 1137605: Prove the following using mathematical induction. Be sure to show the anchor as well as
the full induction steps. Please show all the parts to the
proof.
3+7+11+...+(4n-1)=n(2n+1)
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Base case: n=1
LHS: 3
RHS: 1(2*1+1) = 1(3) = 3

Hypothesis: 3+7+11+...+(4k-1) = k(2k+1)

Must show the above is true for n=k+1
3+7+11+...+(4k-1)+(4(k+1)-1) =

+ (4(k+1)-1)
By hypothesis, the green terms are k(2k+1), so we write
=
=
=
=
(n=k+1)
= DONE

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