Question

1/2*4+1/4*6+1/6*8+......+1/98*100怎样解？

急急急

Answer 1

因为1/n(n+2)=[1/n-1/(n+2)]/2

所以
1/2*4+1/4*6+1/6*8+......+1/98*100
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+...+1/2*(1/98-1/100)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+...+1/98-1/100)
=1/2*(1/2-1/100)
=49/200.

Answer 2

1/2*4+1/4*6+1/6*8+......+1/98*100
=1/4[1/1*2+1/2*3+1/3*4+......1/49*50}
=1/4[1-1/2+1/2-1/3+1/3-1/4+......+1/49-1/50]
=1/4[1-1/50]
=49/200

Answer 3

1/n×（n+1）=（n+1-n）/n×（n+1）=1/n-1/(n+1)
原式=1/2*(1/1*2+...+1/49*50)=1/2*(1-1/50)=49/100

Answer 4

1/2*4+1/4*6+1/6*8+......+1/98*100怎样解？
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+… …+1/98-1/100)
=1/2(1/2-1/100)
=1/2*49/100
=49/200