Induction: (p - 1)(p + 1)

[solomon_13000]

(p - 1) (2 ^ p x 2) + 2 + (p + 1)(2 ^ p x 2)

does (p - 1) and (p + 1) become (p - 1) as in

(p - 1)(2 ^ p x 2) + 2

 

[stapel]

Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of your work and reasoning (from the beginning), so we can see how you arrived at this stage.

Thank you.

Eliz.

 

[Denis]

Re: Induction (p - 1)(p + 1)

(p - 1) (2 power p x 2) + 2 + (p + 1)(2 power p x 2)

does (p - 1) and (p + 1) become (p - 1) as in

(p - 1)(2 power p x 2) + 2

Unclear. Please repost.
For multiplication, use * (not x; x could be a variable)
For power, use ^ ; like 2 to power p : 2^p

 

[solomon_13000]

Proof:

1 + 8 + 24............(n.2 power n) = (n - 1)(2 power n + 1) + 2

 

[stapel]

Proof:

1 + 8 + 24............(n.2 power n) = (n - 1)(2 power n + 1) + 2

I will guess that the decimal point is meant to be a "times" sign, so you're actually working with:

. . . . .Prove that 1 + 8 + 24 + ... + (n)(2^n) = (n - 1)(2^n + 1) + 2

(I have guessed as to your meaning on the "powers". As has been requested earlier, using standard notation and grouping symbols would go a long way toward making your meaning clear.)

I'm afraid that I cannot figure out how you arrived at your original question. What do you mean, when you ask whether p + 1 "becomes" p - 1?

When you reply, please show all of your work and reasoning, following the general outline for induction proofs explained in another of your threads.

Thank you.

Eliz.