六年级数学题1*2分支1+2*3分支1+3*4分支1++...39*40分支1是多少?
2019-05-22
六年级数学题1*2分支1+2*3分支1+3*4分支1++...39*40分支1是多少?
优质解答
1/(1*2)+1/(2*3)+1/(3*4)+.+1/(39*40)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/39-1/40)
=1-1/2+1/2-1/3+1/3-1/4+.-1/39+1/39-1/40
=1+0+0+0+.-1/40
=1-1/40
=39/40
1/(1*2)+1/(2*3)+1/(3*4)+.+1/(39*40)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/39-1/40)
=1-1/2+1/2-1/3+1/3-1/4+.-1/39+1/39-1/40
=1+0+0+0+.-1/40
=1-1/40
=39/40