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Convergence of Power Series

1 Determine whether the series converges absolutely, converges conditionally, or diverges.
Σ 2∙4∙6∙∙(2n)/2ⁿ(n+2)!

2 Calculate sin 87° accurate to five decimal places using Taylor's formula for an appropriate function centered at x = pi/2.

3 Find the interval of convergence of the power series

Σ 2ⁿx2n/n^3

Solution Preview

1. We note that 2*4*6*...*2n = 2^n*n!, then
an = 2*4*6*...*2n / 2^n*(n+2)! = 1/(n+1)(n+2) < 1/n^2
and sum(n from 1 to oo) 1/n^2 is convergent.
Thus the series is convergent. Because this is a positive series,
then it also ...

Solution Summary

Convergence of Power Series are investigated.