1/3+1/(3+6)+1/(3+6+9)+1/(3+6+9+12)+1/(3+6+9+12+15)+.1/(3+6+9+12+15+.96+99)
问题描述：
1/3+1/(3+6)+1/(3+6+9)+1/(3+6+9+12)+1/(3+6+9+12+15)+.1/(3+6+9+12+15+.96+99)
答
你知道等差数列吗？
3+6+9+……+3N=（3+3N）N/2
所以1/（3+6+9+……+3N）=(1/n-1/n+1)*2/3
所以原来就等于
2/3(1-1/2+1/2-1/3+1/3-1/4+……+1/33-1/34)=2/3*(1-1/34)=2/3(33/34)=11/17
答
=( 1/1+1/(1+2)+````+1/(1+2+3`+```+33) ) /3
=( 2/1*2+2/2+3+2/3*4+...+2/33*34 ) /3
=2/3 (1-1/2+1/2-1/3+1/3-1/4.+1/33-1/34)
=2/3 (33/34)
=11/17
原理等差求和公式+列项求和