Question

1/Tính nhanh

P=(1-\(\frac{1}{2^2}\)) x (1-\(\frac{1}{3^2}\)) x (1-\(\frac{1}{4^2}\)) x ... x (1-\(\frac{1}{50^2}\))

2/Cho Q=(1-\(\frac{1}{2^2}\)) x (1-\(\frac{1}{3^2}\)) x (1-\(\frac{1}{4^2}\)) x ... x (1-\(\frac{1}{40^2}\)) . So sánh Q với \(\frac{1}{2}\)

3/So sánh: A = \(\frac{2016^{2016}+1}{2016^{2017}+1}\)và B = \(\frac{2016^{2017}-3}{2016^{2018}-3}\)

Answer 1

 P \(=\left(1-\frac{1}{2^2}\right).\left(1-\frac{1}{3^2}\right).\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{50^2}\right)\) 

P\(=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}...\frac{50^2-1}{50^2}\)

P \(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{49.51}{50.50}\)

P\(=\frac{\left(1.2.3...49\right).\left(3.4.5...51\right)}{\left(2.3.4...50\right).\left(2.3.4...50\right)}\)

P\(=\frac{1.51}{50.2}=\frac{51}{100}\)