X is a complex number. but X is not equal to 1. X^2011=1
Compute the sum
X^(2n)/((x^n)-1) where n=1,2,3...2010
To compute the sum, we need to find the value of the expression for each value of n, and then add them all together.
Let's start by simplifying the expression: X^(2n)/((x^n)-1).
Since we know that X^2011 = 1, we can rewrite X^(2n) as (X^2011)^n/((x^n)-1) = 1^n/((x^n)-1) = 1/(x^n-1).
Now, we can substitute each value of n from 1 to 2010 into the expression and add them together.
For n = 1: 1/(x^1-1) = 1/(x-1)
For n = 2: 1/(x^2-1)
For n = 3: 1/(x^3-1)
...
For n = 2010: 1/(x^2010-1)
To compute the sum, we need to add all these terms together:
Sum = 1/(x-1) + 1/(x^2-1) + 1/(x^3-1) + ... + 1/(x^2010-1)
Please note that without knowing the specific value of x, we cannot simplify the expression further or find the exact value of the sum.