Mathematical induction: = 2 x 2^k+1 - 1

[veritas]

=2 x 2^k+1 - 1
=2^(k-1) +1 -1

Can someone explain to me the computation for getting the answer. As I figured, the 2 was factored, but then why did it become (k-1) +1 instead of (k+1).

Thanks.

 

[Mrspi]

Re: Mathematical induction

=2 x 2^k+1 - 1
=2^(k-1) +1 -1

Can someone explain to me the computation for getting the answer. As I figured, the 2 was factored, but then why did it become (k-1) +1 instead of (k+1).

Thanks.

I guess I have to say "huh????"

Please be very specific about what you are starting with, and what you need to prove. What you have posted here is not enough for ME to see what you're trying to do. Of couse, thre are folks here who have better crystal balls than I do.

 

[Denis]

Double "huh"!

DO NOT use x for multiplication: use *

I think you mean: 2 * 2^(k+1) - 1 which equals 2^(k+2) - 1

Anyway, looking at what you did, I think you need classroom help.

 

[veritas]

Re: Mathematical induction

If you have nothing to say that would help me, then don't comment at all. I don't need derogatory remarks about crystal balls. If you don't want to help, then don't.

And as for me needing classroom help, it's obvious I need help with this or I wouldn't be asking, so don't message me just to tell me I need help.

And this answer is from the book:

2 * 2^(k+1) - 1 = 2^((k-1) + 1) -1

the whole thing (k-1) + 1 is the exponent of 2 in the final answer. I just want to know how they got that answer.

 

[pka]

Re: Mathematical induction

And this answer is from the book: 2 * 2^(k+1) - 1 = 2^((k-1) + 1) -1, the whole thing (k-1) + 1 is the exponent of 2 in the final answer. I just want to know how they got that answer.

It appears that the text book is simply wrong!

If it were 2*2<SUP>k+1</SUP>-1=2<SUP>(k+1)+1</SUP>-1 then it would be true.

 

[Denis]

Re: Mathematical induction

And as for me needing classroom help, it's obvious I need help with this or I wouldn't be asking, so don't message me just to tell me I need help.

Cool it, veritas :idea:

You posted:
2 x 2^k+1 - 1
=2^(k-1) +1 -1

BUT:
2 * 2^k+1 - 1
= 2 * 2^k (since you have no brackets)

So it APPEARED YOU did not know how to solve something simple;
if that was the case, then you WOULD need classroom help, which
simply means it is impossible to teach HERE. Good luck.

 

[stapel]

If you have nothing to say that would help me, then don't comment at all.

For the tutors to be able to assist you, they need to be able to understand what the question is. As posted, your "question" was unintelligible. It is to be regretted if their requests for clarification caused you offense, but I'm afraid that, lacking telepathy ("crystal balls"), there is no way, other than asking you, for them to learn what you meant.

If you are needing a tutor who can figure out what the questions are without your having to communicate them, then you would be needing an in-person tutor, who can read the questions for himself. Your local university's math department, or the guidance counsellor at your local high school, should be able to provide you with information regarding local tutors and their hourly rates.

Thank you.

Eliz.