Answer:
-∞ < x < ∞
Step-by-step explanation:
∑ xⁿ / n^(2ⁿ)
Apply ratio test:
lim(n→∞) | [xⁿ⁺¹ / (n+1)^(2ⁿ⁺¹)] / [xⁿ / n^(2ⁿ)] |
lim(n→∞) | [xⁿ⁺¹ / (n+1)^(2ⁿ⁺¹)] × [n^(2ⁿ) / xⁿ] |
lim(n→∞) | x n^(2ⁿ) / (n+1)^(2ⁿ⁺¹) |
0
The series converges for all values of x.
