First, what happens when you use the distributive property on the product ?
Second, what is the value of when n=0?
I am having trouble solving a problem involving a series.
The problem is the following:
The problem wants me to rewrite the given expression as a sum who generic term involves
For some reason I can't get the same answer that is in the back of the book. I especially don't know what to do when I have the variable "n" with the variable "k". I've tried substituting (n+1) in the place of "n" but that still does work. That method worked in similar problems, so I feel I'm missing out on a subsequent step.
Can anyone please explain thi s to me?
If I factor the "x" in using the distributive property, I get the following result:
with the index of summation set equal to zero, correct? If n=0 in the above variables, then the whole thing is equal to zero?
I'm still confused. I know the answer is supposed to be . I can get everything to look right by using n = (n+1) except for the part. I figured it would be but it is not. I'm guessing the has something to do with it.
My first hint was that .
The second was to note that
Since the n=0 term (not the entire sum, just that one term) is zero, we can add it to the series without changing the value of the series.
Thus, we go from
Now, just rename the variable "k" to "n"
and combine the sums, grouping terms of the same n
Does that make sense?