How do you find a power series representation for x^2 / ( 1 - 2x )^2?
1 Answer
Explanation:
The idea is to relate this expression to the known power series expansion
Temporarily disregard the
Take the integral of
Quick substitution:
Thus, knowing that differentiating this integrated expression returns the original
Let's find the power series representation for the differentiated expression:
We can easily relate
So,
We can absorb the
Differentiate the summation with respect to
Multiply in the