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Another Summation Formula

Another formula you may have seen before is

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One way to prove this is to let S be the sum. Then

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Subtracting them yields

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You might recognize this formula in another guise. Change n+1 to n and multiply both sides by 1-r to get

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Some special cases of this are when n=2,3,4:

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You should recognize these as special cases of some formulas you learned when factoring polynomials.



Carl Lee
Wed Apr 21 08:17:28 EDT 1999