已知n∈N+,n≥2,求证：cos1/2·cos1/3…cos1/n＞2/3

1.只需证明ln[cos1/2·cos1/3…cos1/n]>ln[2/3]=-0.405465108..用常见不等式(大学):ⅰ.当0≤x,cosx≥1-x^2/2 ⅱ.当0≤x≤1/8,ln(1-x)≥-8x/7 还用常见等式:(1/1^2)+(1/1^2)+(1/2^2)+(1/3^2)+..+(1/n^2)+..=π^2/6 2....