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January 28th, 2010, 12:04 AM  #1 
Member Joined: Nov 2009 Posts: 49 Thanks: 0  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." 
January 28th, 2010, 04:54 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  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(n²)+y(n) Now what you're supposed to do is say 1+2+3 = 6, therefore 6 = x(3²)+y(3) = 9x+3y 1+2+3+4 = 10, therefore 10 = x(4²)+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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