(n-1)/n!=n/n!-1/n!=1/(n-1)!-1/n!1/2!+2/3!+3/4!+.....+(n-1)/n!=(1/1!-1/2!)+(1/2!-1/3!)+(1/3!-1/4!)+......+[1/(n-1)!-1/n!]=1-1/n!=(n!-1)/n!
