Dear forum members,

please can someone help me to understand how to do this problem

Determine the sum of all quotients where m and n are whole numbers and

I don't understand how to do this.

Any help is appreciated.

Thank you in advance!

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- Mar 29th 2008, 06:09 AMCoachArithmetic sums
Dear forum members,

please can someone help me to understand how to do this problem

Determine the sum of all quotients where m and n are whole numbers and

I don't understand how to do this.

Any help is appreciated.

Thank you in advance! - Mar 29th 2008, 06:25 AMmr fantastic
- Mar 29th 2008, 07:24 AMCoach
Thank you so much!

Now I get the method. But won't it be quite a long calculation, even if using the arithmetic formula. My teacher wrote a "short cut" on a sample answer sheet as follows

the i-1 should be above the sigma sign, and the k=1 below, and there should be no equal sign before the k, but I just can't get it to work like that. Hope it is still clear enough.

Can you please help me figure out what he is trying to tell?

I noticed that the amount numbers in brackets after the fraction multiplier, are always one less in amount than the numerator of the fraction, but I don't know how to make use of that when creating a shortcut to calculate the sum. - Mar 29th 2008, 08:20 AMMoo
Hello,

Did you understood why he gave this formula ? I'll try to explain a part of it...

This is because in a first time, you sum the fractions while variating the numerator, then when variating the denominator.

The numerator is, as Mr F mentioned the sum of the terms of an arithmetic sequence.

The thing is, normally, it's n(n+1)/2, with n the number above the sign sum (can't find a noun about it)

So here, it's (i-1)(i-1+1)/2 according to the formula.

But i-1+1=i

So you can simplify the general term of the sequence.

And you now have to calculate - Mar 29th 2008, 10:00 AMPlato
We all have different ways. This is close to your instructor's.