Thread: Summation of a real sequence

While trying to prove a mathematical relationship, I ended up with the following term



Where, F and G represent functions that accept inter arguments and return real numbers.

Now, the final goal of my proof is equal to



Can some one please help me if the above two can be proved to be equivalent. I would really appreciate if you could please illustrate all the intermediate steps in this proof.

Originally Posted by led5v

While trying to prove a mathematical relationship, I ended up with the following term



Where, F and G represent functions that accept inter arguments and return real numbers.

Now, the final goal of my proof is equal to



Can some one please help me if the above two can be proved to be equivalent. I would really appreciate if you could please illustrate all the intermediate steps in this proof.

..

Thanks for your illustrative reply. Now I understand that both of these terms are equal. But still I can't find a formal argument to support this claim.

Can this be proved in a formal manner as well using the rules of summations. I would be really thankful if someone could please point me to a formal proof of this goal.

It seems that the senior members in this forum are thinking that I have got my answer, which is not the case. I am still looking for a formal argument to prove the above clain and have looked into a lot of texts on summations but in vain.

Any help in this regard would be greatly appreciated.
thanks,