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May 15th, 2015, 03:56 AM   #1
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Sequence problems

Hi, I am having difficulty with these 3 problems. Could anyone give me a hand? Thanx for your help
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May 15th, 2015, 05:40 AM   #2
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(2k)^3 - (2k-1)^3 = 12*k^2 - 6*k + 1, so you can rewrite the first as
$$
\sum_{k=1}^m 12k^2 - 6k + 1.
$$

This is equal to a cubic polynomial, and you can find it pretty easily if you know the sum formulas.
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May 15th, 2015, 06:18 AM   #3
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For the first, the sum is 4m³ + 3m², which can be obtained by the method already suggested or proved from scratch by mathematical induction.

For the second, use 1/((k-1)(k)(k+1)) = 1/(2(k-1)) - 1/k + 1/(2(k+1)) to get a telescoping sum.

For the third, if S denotes the required sum, relate 3S - S to a geometric series.
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May 29th, 2015, 03:07 AM   #4
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Quote:
Originally Posted by skipjack View Post
For the first, the sum is 4m³ + 3m², which can be obtained by the method already suggested or proved from scratch by mathematical induction.

For the second, use 1/((k-1)(k)(k+1)) = 1/(2(k-1)) - 1/k + 1/(2(k+1)) to get a telescoping sum.

For the third, if S denotes the required sum, relate 3S - S to a geometric series.
Thankx skipjack! I could solve the first two. However I dont understand what you explained for the third one. Can you show me how you would solve it? Thanks for helping me so often.
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