간소화 2/1!+2/3!+...+n/(n+1)! 1/2!+2/3!+...+n/(n+1)!

간소화 2/1!+2/3!+...+n/(n+1)! 1/2!+2/3!+...+n/(n+1)!

첫 번 째 는 1/2!
n/(n+1)!
=[(n+1)-1]/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=1/n!-1/(n+1)!
그래서=1/1!-1/2!+……+1/n!-1/(n+1)!
=1-1/(n+1)!