Question

奥数数学题1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55简便运算急急急~~~！！！

还有1+(1/1+2)+(1/1+2+3)+(1/1+2+3+4)+...+(1/1+...n-1)+(1/1+...n)

Answer 1

分母：1,3,6,10……n(n+1)/2

∴原式=2/(1*2)+2/(2*3)+2/(3*4)+……+2/(10*11)
=2[(1-1/2)+(1/2-1/3)+……+1/10-1/11]
=2(1-1/11)
=20/11=1又9/11
后面一题跟前面差不多，
原式=1+1/3+1/6+1/10+……+1/(1+……+n)
=2{1/(1*2)+1/(2*3)+……+1/[n(n+1)]}
=2[1-1/2+1/2-1/3+……+1/n-1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1)