Question

H=(1+1/1.3)*(1+1/2.4)*(1+1/3.5)*(1+1/4.6)*(1+1/5.7)

Nhanh đúng mk tick 

Answer 1

Ta có :

\(1+\frac{1}{n\left(n+2\right)}=\frac{n\left(n+2\right)+1}{n\left(n+2\right)}=\frac{n^2+2n+1}{n\left(n+2\right)}=\frac{\left(n+1\right)^2}{n\left(n+2\right)}\)

Áp dụng ta được :

\(H=\frac{2.2}{1.3}\cdot\frac{3.3}{2.4}\cdot\frac{4.4}{3.5}\cdot\frac{5.5}{4.6}\cdot\frac{6.6}{5.7}\)

\(=\frac{\left(2.3.4.5.6\right)\left(2.3.4.5.6\right)}{\left(2.3.4.5\right)\left(3.4.5.6.7\right)}=\frac{6.2}{7}=\frac{12}{7}\)