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Books, Books, Books!
George loves reading books. He reads 100 chapters a day. All the chapters are the same length, 40 pages. But the word number on each page changes. If it was the first page of a chapter it would have one word if it were the second it would have three words, the third page would have six and if it were the fourth page it would have 10. The page number and number of words correspond with each other and there is a distinct formula that would get the answer under any circumstances. What is it?
Hint
The tenth page would have 55 words. The page number=n.Answer
where n = page numberwords = (n(n+1))/2
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just add up the page numbers to get the number of words. for instance page 1 has 1 word. page 2 has 1+2 = 3 words. page 3 has 1+2+3 = 6 words. and so on. using the formula, "n2" should be written n^2 (otherwise, it is mistaken for n times 2; the '^' indicates that it is raised to a power). The way you have it written [n2-(n2-1/2n2)+1/2n] reduces out to 1/2n(n+1). I liked it =)
These are triangular numbers 1,3,6,.....etc. The easiest way to generate these is n(n+1)/2. Thus the 10th page would have 10x11/2=55 words.
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