What is the interval of convergence for the power series which begins 1 minus x plus x squared over 2 factorial plus x to the 4th power over 4 factorial and so on ?

Question

What is the interval of convergence for the power series which begins  ? (2 points)

A	(-1, 1)
B	All reals
C	[-1, 1)
D	(-1, 1]

Answer 1

By limit ratio test lim n → ∞ x^{2(n + 1)}/[2(n + 1)]!/(x²ⁿ/(2n)! = lim n → ∞ x²/[(2n + 1)(2n + 2)] = 0 < 1

for any real number x. So, interval of convergence is (- ∞, ∞).

Answer is B