Question

Câu 1 :  Tính hợp lí :

a. A=2011.2011 + 503,4/ 2013. 2011 - 402,5

b. B=3/1.4 + 27/4.7 + 69/7.10 + ... + 867/28.31

Answer 1

tui chỉ làm phần b thôi há !

B=\(\frac{3}{4}\)+\(\frac{27}{28}\)+\(\frac{69}{70}\)+...+\(\frac{867}{868}\)=\(\frac{4-1}{4}\)+\(\frac{28-1}{28}\)+\(\frac{70-1}{70}\)+...+\(\frac{868-1}{868}\)

= 1+1+..+1 -(\(\frac{1}{4}\)+\(\frac{1}{28}\)+\(\frac{1}{70}\)+...+\(\frac{1}{868}\)) = 10 - \(\frac{1}{3}\)(\(\frac{3}{1.4}\)+\(\frac{3}{4.7}\)+\(\frac{3}{7.10}\)+...+\(\frac{3}{28.31}\))

=10-\(\frac{1}{3}\)(1-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{10}\)+...+\(\frac{1}{28}\)-\(\frac{1}{30}\))=10-\(\frac{1}{3}\)(1-\(\frac{1}{30}\))=10-\(\frac{1}{3}\).\(\frac{29}{30}\)=10-\(\frac{29}{30}\)=\(\frac{271}{30}\)