1/2!+2/3!+3/4!+.+n/(n+1)!
=1/2!+2/3!+3/4!+.+n/(n+1)!+1/(n+1)!-1/(n+1)!
=1/2!+2/3!+3/4!+.+1/n!-1/(n+1)!
=1-1/(n+1)!详细点，我看不懂1/2!+2/3!+3/4!+.....+1/n!=1不懂1/2!+2/3!+3/4!+.....+(n-1)/n!+n/(n+1)!=1/2!+2/3!+3/4!+.....+(n-1)/n!+n/(n+1)!+1/(n+1)!-1/(n+1)!=1/2!+2/3!+3/4!+.....+(n-1)/n!+(n+1)/(n+1)!-1/(n+1)!=1/2!+2/3!+3/4!+.....+(n-1)/n!+1/n!-1/(n+1)!=1-1/(n+1)!从后往前消项,明白了吧明白