BackRadius and interval of convergence Use the Ratio Test or the Root Test to determine the radius of convergence of the following power series. Test the endpoints to determine the interval of convergence, when appropriate.
x +x³/3 +x⁵/5 +x⁷/7 + ...
Suppose the power series ∑ₖ₌₀∞ cₖ(x−a)ᵏ has an interval of convergence of (−3,7]. Find the center a and the radius of convergence R.
Suppose a power series converges if |x−3|<4 and diverges if |x−3| ≥ 4. Determine the radius and interval of convergence.
Is ∑ₖ₌₀ ∞ (5x − 20)ᵏ a power series? If so, find the center a of the power series and state a formula for the coefficients cₖ of the power series.
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₀∞ k(x−1)ᵏ
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₀∞ (k²⁰ xᵏ)/(2k+1)!
Radius of convergence Find the radius of convergence for the following power series.
∑ₖ₌₁∞ (k!xᵏ)/(kᵏ)
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₀∞ (-x/10)²ᵏ
Radius of convergence Find the radius of convergence for the following power series.
∑ₖ₌₁∞ (1−cos (1/2ᵏ)) xᵏ
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₀∞ (2x)ᵏ
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₁∞ (kx)ᵏ
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₁∞ sinᵏ(1/k) xᵏ
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₀∞ (x/3)ᵏ
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₁∞ (xᵏ/kᵏ)
Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
∑ₖ₌₀∞ (2x)ᵏ/k!