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January 28th, 2010, 12:04 AM   #1
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what the hell do I do

Can someone please explain to me what this question wants?

"The sum of the first n natural numbers is equal to the sum of two quantities, the first of
which is proportional to n and the second to n2. Work out the sums of the first three and
four natural numbers and hence find the formula for the sum of the first n natural numbers."
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January 28th, 2010, 04:54 AM   #2
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Re: what the hell do I do

There are two numbers x and y such that, for all whole numbers n,
1+2+3+4+5+...+n = x(n)+y(n)

Now what you're supposed to do is say

1+2+3 = 6, therefore
6 = x(3)+y(3) = 9x+3y

1+2+3+4 = 10, therefore
10 = x(4)+y(4) = 16x+4y

So you have 9x+3y=6 and 16x+4y=10, which you must solve for x and y.
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