Question

根据高斯定理解答一道数学难题求1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4

Answer 1

1+2+3+...+n=n(n+1)/2

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

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+100)

=2[1-1/2+1/2-1/3+1/3-.+1/100-1/101]

=2*100/101

=200/101