Thread: challenging factorial problem

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...

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...