√(1+1/1²+1/2²)+√(1+1/2²+1/3²)+…+√﹙1+1/2003²+1/2004²)=

问题描述:

√(1+1/1²+1/2²)+√(1+1/2²+1/3²)+…+√﹙1+1/2003²+1/2004²)=

∵1+1/n^2+1/(n+1)^2={[n(n+1)]^2+(n+1)^2+n^2}/[n(n+1)]^2={[n(n+1)]^2+[(n+1)^2-2n(n+1)+n^2]+2n(n+1)}/[n(n+1)]^2={[n(n+1)]^2+2n(n+1)+[(n+...