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

Answer 1

Here is the end fraction
\(\dfrac{4(4n+1)(8n+7)}6\)

Answer 2

But.. I can't.. Jess D:

@Luigi0210

Answer 3

Sammi... tsk tsk tsk
I was counting on you :(

Answer 4

From what I can tell from the lessons, I just replace n with 1 and see if it equals 4, n with 2 see if it is 6, etc

Answer 5

I'm trying to remember how to do this.. this stuff is old to me xD

Answer 6

Yea, the first thing to do would be to plug in n=1 to see if the statement is true.

Answer 7

ok, I got 60 for n = 1, but if it is true, is it supposed to equal 4 or 24?

Answer 8

\[\frac{4(4 \times 1+1)(8(1)+7)}{6}=\frac{4 \times 5 \times 15}{6}=50\]
Can't remember how to do left side for n=1

Answer 9

ah whoops, I must have gotten confused haha, yes it would be 50 not 60 :)

Answer 10

@ganeshie8 could you please help?

Answer 11

for \(n=1\) left hand side contains just the first term : \(4\cdot 6\)

Answer 12

So if it were true, then for n = 1 on the right, it should equal to 24?

Answer 13

Yes clearly the given statement is false for \(n=1\). So we're done.

Answer 14

Ok, thank you :)

Answer 15

yw:)