Tìm stn n thỏa mãn đk: \(2.2^2+3.2^3+4.2^4+..+n.2^2=2^{n+16}\)

Tính: \(A=\dfrac{34}{7.13}+\dfrac{51}{13.22}+\dfrac{85}{22.37}+\dfrac{68}{37.49}\)

\(\dfrac{3}{4}+\dfrac{1}{3}-\left(\dfrac{7}{4}-\dfrac{5}{3}+\dfrac{3}{7}\right)\\ =\dfrac{3}{4}+\dfrac{1}{3}-\dfrac{7}{4}+\dfrac{5}{3}-\dfrac{3}{7}\\ =\left(\dfrac{3}{4}-\dfrac{7}{4}\right)+\left(\dfrac{1}{3}+\dfrac{5}{3}\right)-\dfrac{3}{7}\\ =-1+2-\dfrac{3}{7}\\ =1-\dfrac{3}{7}\\ =\dfrac{4}{7}.\)

Tính giá trị của biểu thức sau: \(A=-\dfrac{1}{5}+\dfrac{1}{5^2}-\dfrac{1}{5^3}+...+\dfrac{1}{5^{100}}\)