Is this series absolutely convergent 2/5 + (2*6)/(5*8) + (2*6*10)/(5*8*11) + (2*6*10*14)/(5*8*11*14) + ...
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Originally Posted by amiv4 Is this series absolutely convergent 2/5 + (2*6)/(5*8) + (2*6*10)/(5*8*11) + (2*6*10*14)/(5*8*11*14) + ... Using the Ratio Test givse Therefore your series diverges.
Last edited by Mathstud28; Nov 11th 2008 at 01:16 PM. Reason: typo
shouldnt it be 4k +2 in the first part instead of 2k+4. and i think that messes everything else up
Originally Posted by amiv4 shouldnt it be 4k +2 in the first part instead of 2k+4. and i think that messes everything else up Yes, that was a typo. The solution still holds.
k I'm really not seeing how when u multiply those two together you get that. Cuz i did the ratio test myself and i dont see how those multiply together to get that. Can you explain
Let's write it explicitly. Let: Using the ratio test, (simply what is) (simplified the brackets) (expanded the inside of the dots) Notice that the red's and blue's cancel out. Take the limit of what remains and the rest follows (see Mathstud's post).
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