1/3+1/(2*4)+1/(3*5)+1/(4+6).+1/(19*21)+1/(20*22)
问题描述:
1/3+1/(2*4)+1/(3*5)+1/(4+6).+1/(19*21)+1/(20*22)
答
1/3+1/(2*4)+1/(3*5)+1/(4+6).+1/(19*21)+1/(20*22)=1/2×(1-1/3+1/.3-1/5+……1/19-1/21)+1/2×(1/2-14+1/4-1/6+……+1/20-1/22)=1/2×20/21+1/2×10/22=10/21+5/22=325/4621/3+1/(2*4)+1/(3*5)+1/(4+6)......+1/(19*21)+1/(20*22)为什么==1/2×(1-1/3+1/.3-1/5+……1/19-1/21)+1/2×(1/2-14+1/4-1/6+……+1/20-1/22)=1/2×20/21+1/2×10/22=10/21+5/22=325/462