Question

Tính hợp lí:

A=\(\left(-2\right).(-1\dfrac{1}{2}).\left(-1\dfrac{1}{3}\right).\left(-1\dfrac{1}{4}\right)........\left(-1\dfrac{1}{2008}\right)\)

Answer 1

\(A=\left(-2\right)\left(-1\dfrac{1}{2}\right)\left(-1\dfrac{1}{3}\right)\left(-1\dfrac{1}{4}\right)...\left(-1\dfrac{1}{2008}\right)\)

\(A=-2.\dfrac{-3}{2}.\dfrac{-4}{3}.\dfrac{-5}{4}.......\dfrac{-2009}{2008}\)

\(A=\dfrac{-2}{1}.\dfrac{-3}{2}.\dfrac{-4}{3}.\dfrac{-5}{4}......\dfrac{-2009}{2008}\)

Từ \(-2\) đến \(-2009\) có số số hạng là:

\(\left(2009-2\right):1+1=2008\)

\(2008\) là số chẵn nên:

\(A=\dfrac{2.3.4.5.....2009}{1.2.3.4.....2008}\)

\(A=2009\)