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Series

Can someone check if I have dine this correctly. I may have done useless working.
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Reply 1
Yes, but there is some pointless working. You can pretty much just say tha a_n converges to 0, and that it is decreasing. Your method of showing it doesn't do it any better.

Otherwise it is fine, and it does work, although you may want to state more explicitly that it is decreasing.
Original post by james22
Yes, but there is some pointless working. You can pretty much just say tha a_n converges to 0, and that it is decreasing. Your method of showing it doesn't do it any better.

Otherwise it is fine, and it does work, although you may want to state more explicitly that it is decreasing.


When I was doing it I was thinking of the series of 1/n^a where a <0 which diverges. I was thjnkibg that thos applied to normal sequences too. I was confused. Thanks though.

Posted from TSR Mobile
Original post by james22
Yes, but there is some pointless working. You can pretty much just say tha a_n converges to 0, and that it is decreasing. Your method of showing it doesn't do it any better.

Otherwise it is fine, and it does work, although you may want to state more explicitly that it is decreasing.


Can you help on this please. Last part. Can I just say that a_n is a monotone sequence increasing and it is bounded by the statement given in part three so a_n must converge. There is a theorem that states this.
Also the series in part three converges too because the power of the k is greater than 1.

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Reply 4
Original post by cooldudeman
Can you help on this please. Last part. Can I just say that a_n is a monotone sequence increasing and it is bounded by the statement given in part three so a_n must converge. There is a theorem that states this.
Also the series in part three converges too because the power of the k is greater than 1.

Posted from TSR Mobile


Yep, you showed that the series converged in part a) anyway.
Original post by james22
Yep, you showed that the series converged in part a) anyway.


Thanks

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