己知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n+1)n=1/n-1-1/n+1
问题描述:
己知1/1x2=1-1/2;1/2x3=1/2-1/3,1/3x4=1/3-1/4,1/4x5=1/4-1/5;…1/(n+1)n=1/n-1-1/n+1
求不等式x/2+x/6+x/12+…+x/9900≯99的解集.
答
x/2+x/6+x/12+…+x/9900≯99
x(1/2+1/6+1/9900)≯99
∴x(1-1/2+1/2-1/3+……+1/99-1/100)≯99
99/100x ≯99
x≯100