1/{2^2+4]+ 1[/4^2+8]+1/[6^2+12]+...+1/[(2n)^2+4n]consider1/[(2n)^2+4n]=1/[4n(n+1)]=(1/4)[1/n -1/(n+1)]1/{2^2+4]+ 1[/4^2+8]+1/[6^2+12]+...+1/[(2n)^2+4n]=(1/4) [ (1/1-1/2)+(1/2-1/3)+...+(1/n-1/(n+1)]=(1...