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

@helder_edwin

Answer 2

now. do u see the term 4n(4n+2) on the left side of the equation??

Answer 3

Yes. That's actually what it says in the problem.

Answer 4

this small formula is supposed to prepoduce all the termns on the left.

Answer 5

if n=1 u get
\[ \large 4\cdot1(4\cdot1+2)=4\cdot(4+2)=4\cdot6 \]
which is fine. it is the first term.
OK?

Answer 6

@aleisha0301 ??

Answer 7

Yes I understand so far

Answer 8

the problem is that if u put n=2 u should get the second term but
\[ \large 4\cdot2(4\cdot2+2)=8\cdot(8+2)=8\cdot10 \]
which is not the second term !!!!

Answer 9

So therefore the statement is false?

Answer 10

it is either that or the problem is ill-posed.

but let's write down that it is false.

Answer 11

Yes that's the easier answer haha. But I have one last problem. Would you mind helping me solve it?

Answer 12

not at all.

but perhaps u could check the problem with one of your classmates. just to be sure.

Answer 13

Unfortunately this is an online class :/

Answer 14

oh.
then let's try the other problem u mentioned.

Answer 15

Alrighty