a1=1/4f(1)=1-a1=3/4a2=1/9f(2)=3/4×8/9=2/6=1/3a3=1/16 f(3)=1/3 × 15/16=5/16.推導(dǎo)f(n)的值：a(n)=1/(n+1)^2設(shè)b(n)=1-a(n)=1-1/(n+1)^2=[(n+1)^2-1]/(n+1)^2=n(n+2)/(n+1)^2f(n)=b(1)×b(2)×...×b(n)=1×3/2&#...f(2)=3/4×8/9=2/6=1/3不是等于2/3嗎？sorry，算錯了，不過下面的沒錯a1=1/4 f(1)=1-a1=3/4a2=1/9 f(2)=3/4×8/9=2/3a3=1/16 f(3)=2/3 × 15/16=5/8推導(dǎo)f(n)的值：a(n)=1/(n+1)^2設(shè)b(n)=1-a(n)=1-1/(n+1)^2=[(n+1)^2-1]/(n+1)^2=n(n+2)/(n+1)^2f(n)=b(1)×b(2)×...×b(n)=1×3/2²× 2×4/3²×...× n(n+2)/(n+1)²=[3/2×4/3×5/4×6/5×...×(n+1)/n]×(n+2)/(n+1)²=(n+1)/2×(n+2)/(n+1)²=(n+2)/[2(n+1)]