Question

Tính giá trị biểu thức:

\(B=\left(1-\frac{1}{^{2^2}}\right).\left(1-\frac{1}{3^2}\right).....\left(1-\frac{1}{2010^2}\right)\)

Answer 1

\(B=\left(\frac{2^2-1}{2^2}\right)\left(\frac{3^2-1}{3^2}\right)...\left(\frac{2010^2-1}{2010^2}\right)\) 

\(B=\left(\frac{\left(2-1\right)\left(2+1\right)}{2^2}\right)...\left(\frac{\left(2010-1\right)\left(2010+1\right)}{2010^2}\right)\)

\(B=\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{2009.2011}{2010.2010}\)

\(B=\left(\frac{1}{2}.\frac{2}{3}...\frac{2009}{2010}\right)\left(\frac{3}{2}.\frac{4}{3}...\frac{2011}{2010}\right)\) 

\(B=\frac{1}{2010}.\frac{2011}{2}\)

\(B=\frac{2011}{4020}\)