求计算,1/3 +1/3+6 +1/3+6+9 +.+1/3+6+9+.+99 空格是分开符号,极速解.
问题描述:
求计算,1/3 +1/3+6 +1/3+6+9 +.+1/3+6+9+.+99 空格是分开符号,极速解.
快,快答,答对有+赏.
答
原式
=(1/3)[1+1/(1+2)+1/(1+2+3)+······+1/(1+2+3+······+33)]
=(1/3)[2/(2×1)+2/(3×2)+2/(4×3)+······+2/(34×33)]
=(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.