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AmTran_Bus
 one year ago
Interval of convergence Check work
AmTran_Bus
 one year ago
Interval of convergence Check work

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AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438630716254:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0$$\frac{\sqrt[4]{n+1}\,(x6)^{n+1}}{\sqrt[4]n\ (x6)^n}=\sqrt[4]{1+\frac1n}\cdot (x6)$$so the ratio test shows $$\lim_{n\to\infty}\sqrt[4]{1+\frac1n}\cdot \leftx6\right=x6<1$$ so we know the radius of convergence is \(R=1\). now we test the boundary points: for \(x=5\) we have $$\sum_{n=0}^\infty \sqrt[4]{n}(1)^n$$ since \((1)^n\sqrt[4]{n}\not\to 0\) it diverges. similarly for \(x=7\) $$\sum_{n=0}^\infty\sqrt[4]{n}$$ again, \(\sqrt[4]\not\to 0\) so it diverges

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0again, \(\sqrt[4]{n}\not\to 0\) so it diverges * i meant to say

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Ok. Check this tho http://www.wolframalpha.com/input/?i=+sum+n%3D1+to+infinity+4th+root%28n%29%28x6%29%29%5En

AmTran_Bus
 one year ago
Best ResponseYou've already chosen the best response.0Because I really thought (5,7) was right after solving the inequality.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1He was agreeing with you it diverges at the endpoints 5 and 7.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1which means it is (5,7) not [5,7] or [5,7) or (5,7]
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