If f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞xn and g(x)=∑n=0∞(−1)nxng(x) = \sum_{n=0}^{\infty} (-1)^n x^ng(x)=∑n=0∞(−1)nxn, what is f(x)+g(x)f(x) + g(x)f(x)+g(x) as a power series?
∑n=0∞2x2n\sum_{n=0}^{\infty} 2x^{2n}∑n=0∞2x2n
∑n=0∞(1+(−1)n)xn\sum_{n=0}^{\infty} (1 + (-1)^n) x^n∑n=0∞(1+(−1)n)xn
2∑n=0∞x2n2\sum_{n=0}^{\infty} x^{2n}2∑n=0∞x2n
All of the above