Ta có:
($\dfrac{1}{2}$ ² - 1) ($\dfrac{1}{3}$ ² -1) ($\dfrac{1}{4}$ ² -1)....($\dfrac{1}{40}$ ² - 1)
=($\dfrac{1}{4}$ -1)($\dfrac{1}{9}$-1)($\dfrac{1}{16}$-1)...($\dfrac{1}{1600}$-1)
=(-$\dfrac{3}{4}$)(-$\dfrac{8}{9}$)(-$\dfrac{15}{16}$)...(-$\dfrac{1599}{1600}$)
Do tích trên có :(40-2):1+1=39(thừa số âm)
Nên tích trên có kết quả âm
⇒=-($\dfrac{3}{4}$·$\dfrac{8}{9}$·$\dfrac{15}{16}$...$\dfrac{1599}{1-600}$)
=-($\dfrac{3·8·15·...·1599}{4·9·16·...·1600}$)
=-($\dfrac{3·2·4·3·5·4·6·...·39·41}{2·2·3·3·4·4·...·40·40}$)
=-($\dfrac{(2·3·4·...·39)·(3·4·5·6·...·41)}{(2·3·4·...·40)·(2·3·4·...·40)}$)
=-($\dfrac{3·41}{40·2}$)
=-$\dfrac{123}{80}$