Question

级数∑【n从1到无穷】{2^(n+1)/3^(n-1) -4/4n^2 -1}的和为?

Answer 1

∑【n从1到无穷】{2^(n+1)/3^(n-1) -4/4n^2 -1}=∑【n从1到无穷】{2^(n+1)/3^(n-1) -∑【n从1到无穷】{4/4n^2 -1]=4∑【n从1到无穷】[2^(n-1)/3^(n-1) -∑【n从1到无穷】2[1/(2n -1)-1/(2n+1)]

=4*1/(1-2/3)-2lim(1-1/(2n+1))=12-2=10