1+1/1+2+1/1+2+3+1/1+2+3+4+.........1/1+2+3+........+1000
=1+1/[(1+2)×2÷2]+1/[(1+3)×3÷2]+1/[(1+4)×4÷2]+........1/[(1+1000)×1000÷2]
=1+2/(1+2)×2+2/(1+3)×3+2/(1+4)×4+........2/(1+1000)×1000
=1+2×(1/2-1/3+1/3-1/4+1/4-1/5+.......+1/1000-1/1001)
=1+2×1/1001
=1又2/1001
化减:2/1*2+2/2*3+2/3*4+…然后列项:(2/1-2/2)+(2/2-2/3)…然后化简:2/1-2/101=200/101 如果取极限得2
1加到一百我知道,就是按顺序加的我知道。比如最后一个数为X,那就是X乘于X加1的和,然后除以2
解:1/1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…1/(1+2+3+4+5+…100)
=2{1/(1×2)+1/(2×3)+…+1/[100(100+1)]}
=2[1-1/2+1/2-1/3+…+1/100-1/(100+1)]
=2[1-1/(100+1)]
=2*100/(100+1)
=200/101 如何?
1+1/(1+2)+1/(1+2+3+4)+1/(1+2+3+4+......+1/(1+2+3+......100