Find the radius of convergence R of the series.

Question

Please find the "radius of convergence" for the following function: 6 / (1 + 49x^2) represented by the following power series:

Answer 1

Look up the series for (1+t)^a.

You will see that it converges for |t|<1.

Therefore the radius of convergence is |49x²|<1, i.e. |x|<1/7.