Thread: integral, power series

I've never been very good at integrals, i need help with this one please.

Evaluate the indefinite integral as a power series. What is the radius of convergence?

INT t/(1 - t^4) dt

thanks.

Originally Posted by rcmango

I've never been very good at integrals, i need help with this one please.

Evaluate the indefinite integral as a power series. What is the radius of convergence?

INT t/(1 - t^4) dt

thanks.

INT t/(1 - t^4) dt = integral t + t^5 + t^9 + .. + t^{4n-3} + ... dt

.........................= t^2/2 + t^6/2 + ... + t^{4n-2)}/(4n-2) + ..

........................= Sum_{n=1, infty} t^{4n-2)}/(4n-2)

and its radius of convergence should be |t|<1.

RonL