Math Is Fun Forum

CandyManSugar

Member

Registered: 2014-05-22

Posts: 3

Series and Sequence

The terms of a particular sequence can be generated from its recurrence relation which is given as

 

with

Find the value of the following sum

(A) 1
(B) -1
(C) 0
(D) None of those

This question is not appearing properly in the post because some are in superscript and some are in subscript. If you want a clear version I can email screen shot.

Hope some would be able to help me also would be much grateful if someone can provide me with complete solution.

Regards,

Candy Man

Last edited by CandyManSugar (2014-05-22 22:26:46)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Series and Sequence

Hi;

Hope some would be able to help me also would be much grateful if someone can provide me with complete solution.

I fixed your latex.

Can I see what you have tried? You must do at least some of your own homework. The effort is important.

Did you generate the first 10 values of that recurrence? Did you notice the pattern?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Complexity

Member

From: Denmark

Registered: 2013-12-27

Posts: 16

Re: Series and Sequence

Well you can solve for the solution, right? So we start out by finding the solution of the characteristic equation:

We find the solutions r=3 and r=-1. Hence we get the complete solution:

By inserting the values you've been given we obtain:

and

Solving these equations we get that

and

Hence the formula we obtain is:

If we have to add A_1, A_2...A_n, the we will get either 0 or -1. If n is an odd number, then we will get -1 as an result, and 0 if n is even.

Last edited by Complexity (2014-05-23 00:26:03)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Series and Sequence

Or you could notice the pattern. -1,1,-1,1... This must continue. We have 500 pairs of -1,1 which cancel and one -1 leftover. The sum is -1.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.