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Use Mathematical Induction to Prove the Statement Is True for All

Question 30

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Use mathematical induction to prove the statement is true for all positive integers n.
- 5⋅7+6⋅8+7⋅9+…+5n(5n+2)=5n(5n+1)(10n+7)65 \cdot 7 + 6 \cdot 8 + 7 \cdot 9 + \ldots + 5 n ( 5 n + 2 ) = \frac { 5 n ( 5 n + 1 ) ( 10 n + 7 ) } { 6 }

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