- #1
courtrigrad
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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?
(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
(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