### Author Topic: Help with solving recursive equations (ive done all the work already)  (Read 1973 times)

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#### Dreyth

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• Respect: +992 ##### Help with solving recursive equations (ive done all the work already)
« on: February 18, 2013, 01:44:48 pm »
0 2 things I want to understand. They both reside in the telescoping:

(1) Why are all those steps equal to 1 in the telescoping?
(2) Why is the last step in the telescoping equal to k?

My only guess for (2) is that the reason it's equal to K is because in the two equations:

S(0) = 1
S(k) = S(k-1) + 1, k>0

k is what we are solving for in the first place. Is that why k is at the end of the telescoping?
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#### Dreyth

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• Respect: +992 ##### Re: Help with solving recursive equations (ive done all the work already)
« Reply #1 on: February 18, 2013, 03:23:59 pm »
0
Never mind, i've figured it out on my own!

you get the =1 from rearranging S(k) = S(k-1) + 1 into S(k) - S(k-1) = 1
and all the sums add up to k because you are taking the summation of 1+1+1... k times since you have k equations.
« Last Edit: February 18, 2013, 03:26:26 pm by Dreyth »
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