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Calculus/Sigma Notation

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Expert: - 2/13/2011


Question
592
Z (5k + 2j)=
k=126

This is a summation problem. I'm stumped. HELP

Answer
It is known that j is a variable and the total number of j's is always 2 every time,
so the total is (592-126+1)2j = 934j.

For k, the summation from 1 to n of k is n(n+1)/2.
For 5k, the summation from 1 to n of k would then be 5n(n+1)/2.

For k = 126 to 592, this would be the same as the (summation from 1 to 592) -
(summation from 1 to 125).

It is known that the summation from 1 to 592 of 5k is 5*592*593/2 and
the summation from 1 to 125 is 5*125*126/2.

Now 5*592*593/2 = 877,640 and  5*125*126/2 = 39,375, so compute x = 877,640 - 39,375.

Once this is done, the answer is x + 934j,
so you have to do is the subtraction in the last line to get x.

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