If are in AP,where >0, then the value of the expression

up to n terms:

Here are the options:

1.

2.

3.

4.

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- Mar 23rd 2009, 01:37 AMsiddscool19Arithmetic Progression Problem...
If are in AP,where >0, then the value of the expression

up to n terms:

Here are the options:

1.

2.

3.

4. - Mar 23rd 2009, 02:36 AMchisigma
If the sequence is an arithmetic progression then…

Now we arrive to compute the sum in such a way…

Kind regards

- Mar 23rd 2009, 02:58 AMn0083
Throughout we use

(*)

Each addend of,

Now each term has a common denominator namely . Adding each term up we see the middle terms in the numerator cancel leaving,

(**)

using (*) again we have .

Substituting this into (**) we have,

Factoring the denominator we have,

Leaving,

which is answer choice 2 (thanks chisigma) - Mar 23rd 2009, 03:20 AMchisigma
- Mar 23rd 2009, 03:59 AMSoroban
Hello, siddscool19!

Quote:

If are in AP, where , find the value of the expression:

. .

Here are the options:

I don't agree with any of their answers.

Did I miscount?

The term is: .

Multiply top and bottom by:

. .

The series becomes:

. .

Most of the terms cancel out and we are left with: .

This can be simplified further, with our knowledge of AP's.

We know that: .

So the numerator is: .

And the fraction becomes: .

Therefore: .

. . This is closest to their answer-choice (2).

- Mar 23rd 2009, 04:34 AMsiddscool19
The answer given in my answer key is choice 1.

I don't know how to solve it. But the answer is 1) choice.