an=ln(n/(n-1))-1/n 则an在n>1单调递减 令n=1/x (x趋向0+)
lim an=lim(-ln(1-x)-x)=0 则an>0 ln(n/(n-1)>1/n
令bn=(sin^n)/n cn=(cosn)^2/n n>=2
cn-bn=cos2n/n 又cos2n级数收敛
则cos2n/n收敛 且小于0 bn>cn
则bn+cn< ln(n/(n-1) n>=2
2cn< ln(n/(n-1) n>=2
cn< ln(n/(n-1)/2
c2+c3+……cn=(cos2)^2/2+……(cosn)^2/n<lnn/2
(cos1)^2+(cos2)^2/2+……(cosn)^2/n<lnn/2+(cos1)^2<(lnn+1)/2