Let 0<a<1 and consider the series

a^2 + a + a^4 + a^3 + ... +a^(2n) + a^(2n-1) + ...

Show that the Root test applies but the ratio test does not apply.

Thanks in advance :)

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- Nov 15th 2012, 08:51 PMAainaaRozTests for nonabsolute convergence
Let 0<a<1 and consider the series

a^2 + a + a^4 + a^3 + ... +a^(2n) + a^(2n-1) + ...

Show that the Root test applies but the ratio test does not apply.

Thanks in advance :) - Nov 15th 2012, 09:13 PMProve ItRe: Tests for nonabsolute convergence
Is there any reason we can't write this as and state that it is a geometric series with and , therefore the series will be convergent if ?

- Nov 15th 2012, 10:20 PMAainaaRozRe: Tests for nonabsolute convergence
I don't think so. Because the question specifically asks to show that root test applies but ratio test doesn't.