Why is this true? I couldn't find anything on the net about

what is X[n] brainlet? if X[n]=X[-n] and X[0]=0 then it's trivial

>>8939495
It's a generic function.

>>8939495
Also, X[n] has both its even and odd components.

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9KB, 625x372px

>>8939493
If this might help clear things up

the sum from negative infinity to 0 noninclusive can be thought of as half the set of the entire sum.

>>8939517
so why is not X[n]/2 instead of 2*X[n]

>>8939517
because in the index shifting you are dividing by two. you are removing half of the indeces of the whole sum, so to make up for the index shift, you must multiply by 2

>>8939498
>>8939493
I think I'm confused.
Define X such that
X[1] = 1
X[-1] = -1
for all other n X[n] = 0
1+-1 =/= 2*1

>>8939525
this was meant to reply to >>8939522

>>8939525
You've cleared up a reasonable chunk, but can you show a numeric explanation, or would that be too trouble some?

>>8939535
does it matter what x is? it shouldnt.

>>8939550
i can try a lay explanation. suppose you wanted to sum 100 apples. you know you ought to be counting from 1 apple to 100 apples. but instead, you begin counting from 50 apples. at the end of counting, there is still a total of 100 apples, so you need to multiply your count by the index shift.

so, if we began summing at 50 instead of 1, we would obtain 50 total (50 ... 100), so we multiply it by two for the actual total.

>>8939570
Im not OP, but this makes sense

>>8939570
Clear as day. I'm and engineering student and I'm sure this would be a shame on me for understanding this after this kind of explanation. Thank you however.

>>8939525
but wouldn't the negative values give you a different number that you would be missing.

>>8939535
I see what you mean! it's technically |x[n]|