Question

6. Find the radius of convergence and the interval of convergence of the power series sum_{n=1}^{infty}(-1)^n n^2(x-a)^{2n} where a is a constant. 7. Suppose the radius of convergence of the power series sum_{n=1}^{infty} c_n x^n is P. Then find the radius of convergence of the power series sum_{n=1}^{infty} c_n x^{an} where a is a positive constant.

          6. Find the radius of convergence and the interval of convergence of the power series
sum_{n=1}^{infty}(-1)^n n^2(x-a)^{2n}
where a is a constant.
7. Suppose the radius of convergence of the power series sum_{n=1}^{infty} c_n x^n is P. Then find the radius of
convergence of the power series sum_{n=1}^{infty} c_n x^{an} where a is a positive constant.

6. Find the radius of convergence and the interval of convergence of the power series
sumn=1^infty(-1)^n n^2(x-a)^2n
where a is a constant.
7. Suppose the radius of convergence of the power series sumn=1^infty cn x^n is P. Then find the radius of
convergence of the power series sumn=1^infty cn x^an where a is a positive constant.

Added by Robert M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Mary Wakumoto

Step 1

The power series is given by: $$\sum_{n=0}^{\infty} (-1)^n (r a)^n$$ We can use the Ratio Test to find the radius of convergence. The Ratio Test states that if: $$\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| = L$$ then the series converges if $L < 1$, Show more…

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Find the radius of convergence and the interval of convergence of the power series ̴(-1)^n * (r * a)^n where r is a constant. 7. Suppose the radius of convergence of the power series ̴CnT is P. Then find the radius of convergence of the power series ̴Cn * x where C is a positive constant.