Simplify 2/1! - 3/2! + 4/3! - 5/4! + ... + 2010/2009! - 2011/2010!, where k! denotes the product of all integers from 1 up to k, that is: 1! = 1, 2! =1 * 2 = 2, 3! = 3*2*1 = 6 and so on...
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n varies from 1 to 2010, therefore, the series reduces to, All the intermediate terms vanish, and what survives is Thus the value of this expression is
you might want to try the expansion of Originally Posted by the undertaker Simplify 2/1! - 3/2! + 4/3! - 5/4! + ... + 2010/2009! - 2011/2010!, where k! denotes the product of all integers from 1 up to k, that is: 1! = 1, 2! =1 * 2 = 2, 3! = 3*2*1 = 6 and so on...
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