Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 4(4n+1(8n+7)/6

Question

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 4(4n+1(8n+7)/6

anonymous · Answer

Well, as stated, the LHS of the formula makes no sense as you can't generate 5 x 7 from the 4n(4n+2) pattern - you can only get even numbers that way.

anonymous · Answer

I'm sort of confused right now can you please elaborate?

anonymous · Answer

Usually the construct is that a series - a sum of a sequence of terms - has a 'generic' sequence term indicating the pattern that they all follow. It's this pattern that gets extended to ever larger integer values, so that you can evaluate. Assuming that 4n(4n+2) is that pattern for the Left Hand Side, then 4n can only ever be an even number and 4n+2 likewise - for any integral value of n. And the product of two even numbers also must be even, so how does the 5 x 7 appear in the example ? The product of two odd numbers must be odd, you see.  So, as stated, it's not clear to me how the LHS series is actually defined.

anonymous · Answer

ohh okay so that makes the equation completely false then because it cannot possibly generate a 5 x 7 in the LHS thanks bro