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Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

4 x 6 +5 x 7 + 6 x 8+...+4n(4n+2)= 4(4n+1)(8n+7) / 6

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\text{Proof by induction:}

\text{Test that the statement holds for n = 1}


LHS = 4(4 + 2) = 4(6) = 24

RHS = (4(4 + 1)(8 + 7))/(6) = (20 \cdot 15)/(6) = (300)/(6) \\eq 24

This means that the statement is false, and thus, cannot be proven by induction.
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