Answer:
(a) C
(b) E
Step-by-step explanation:
aₙ = xⁿ / n!
aₙ₊₁ = xⁿ⁺¹ / (n+1)!
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[xⁿ⁺¹ / (n+1)!] / [xⁿ / n!]│
lim(n→∞)│[xⁿ⁺¹ / (n+1)!] × [n! / xⁿ]│
lim(n→∞)│[xⁿ⁺¹ / xⁿ] × [n! / (n+1)!]│
lim(n→∞)│x / (n+1)│
x is a constant, so the limit equals 0 for all values of x. The limit is always less than 1, so the series is convergent.
