Suppose that [tex] \sum_{n=0}^{\infty} c_{n}x^{n} [/tex] converges when [tex] x=-4 [/tex] and diverges when [tex] x=6 [/tex]. What can be said about the convergence or divergence of the following series?(adsbygoogle = window.adsbygoogle || []).push({});

(a) [tex] \sum_{n=0}^{\infty} c_{n} [/tex]

(b) [tex] \sum_{n=0}^{\infty} c_{n}8^{n} [/tex]

(c) [tex] \sum_{n=0}^{\infty} c_{n}(-3)^{n} [/tex]

(d) [tex] \sum_{n=0}^{\infty} (-1)^{n}c_{n}9^{n} [/tex]

So we know that [tex] \sum_{n=0}^{\infty} c_{n}x^{n} [/tex] converges when [tex] -5\leq x\leq5 [/tex], and diverges when [tex] x> 5 [/tex].

(a) Would [tex] \sum_{n=0}^{\infty} c_{n} [/tex] diverge?

(b) This would diverge because [tex] x>5 [/tex]?

(c) This would converge, because [tex] -5<-3<5 [/tex]?

(d) This would diverge because [tex] x>5 [/tex]?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Power Series

**Physics Forums | Science Articles, Homework Help, Discussion**