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!
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.
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.
So you can simplify the general term of the sequence.
And you now have to calculate