If the sequence is an arithmetic progression then…
Now we arrive to compute the sum in such a way…
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,
which is answer choice 2 (thanks chisigma)
Let be the common difference of the AP.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: .
. . This is closest to their answer-choice (2).