Question

数学题（1）1.逆向运算等式1/a-1/b=b-a/ab,如1/12=4-3/3*4=1/3-1/4.根据上述等式计算：

Answer 1

1+1/2+1/6+1/12+...+1/n(n+1)

=1+1/(2*1)+1/(2*3)+1/(3*4)+……1/n*(n+1)

=1+1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)

=2-1/(n+1)

=(2n+1)/(n+1)