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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

Respuesta :

[tex]\text{Proof by induction:}[/tex]
[tex]\text{Test that the statement holds for n = 1}[/tex]

[tex]LHS = 4(4 + 2) = 4(6) = 24[/tex]
[tex]RHS = \frac{4(4 + 1)(8 + 7)}{6} = \frac{20 \cdot 15}{6} = \frac{300}{6} \neq 24[/tex]

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

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