Geometric series.
Hi there. I have some doubts with this exercise. I have to make the summation for:
I've solved this way:
The doubt I've got is about the "negative" part of the summation, I know how to solve the geometric progression, but I'm not sure about the other part. I've proceeded this way:
This is what I did:
I'm not sure about this, may I should do it this other way?:
I mean, taking the values of the sequence for the series for every "i", and making that summation but the accumulation? cause I think it has not much sense what I did before, I mean there is no accumulation for the negative part, right?
Bye there, and thanks for your help.
A solution for those who can't remember the results or requirements for a geometric series.
Let
Remember, is equal to the sum we are to evaluate.
Multiply both sides of equation (1) by .
The series in equation 2 actually starts at , so let's change the index to reflect that.
Separate the first term, , of this series out from the summation.
The above sum is , and so we have:
Solving this for gives
Your formula is correct but that does not give what you have above. When i= 0, , of course, but when i= -1, , when i= -2, , and when i= -3, . I have no idea where you got "2", "7", and "20".
That sum is 1- 3+ 9- 27= -20
I'm not sure about this, may I should do it this other way?:
I mean, taking the values of the sequence for the series for every "i", and making that summation but the accumulation? cause I think it has not much sense what I did before, I mean there is no accumulation for the negative part, right?
Bye there, and thanks for your help.