Ta có :
\(\dfrac{31}{2}.\dfrac{32}{2}.\dfrac{33}{2}.....\dfrac{60}{2}=31.32.33.....\dfrac{60}{2^{30}}\)
(31.32.33....60)(1.2.3....30)/230(1.2.3....30)
= (1.3.5.....59)(2.4.6.....60 )/( 2.4.6....60 ) = 1.3.5....59
\(\Rightarrow P=Q\)
CHỨNG TỎ RẰNG :
\(\dfrac{1}{31}\)+\(\dfrac{1}{32}\)+\(\dfrac{1}{33}\)+\(\dfrac{1}{35}\)+.....+\(\dfrac{1}{148}\)+\(\dfrac{1}{149}\)\(\dfrac{1}{150}\)<\(\dfrac{13}{6}\)
quy đồng
1. \(\dfrac{-5}{14},\dfrac{3}{20},\dfrac{9}{70}\)
2.\(\dfrac{10}{42},\dfrac{-3}{28},\dfrac{-55}{132}\)
3.\(\dfrac{7}{10},\dfrac{1}{33}\)
Thực hiện phép tính ( tính nhanh nếu có thể )
a)\(\dfrac{4}{11}.\dfrac{2}{5}+\dfrac{4}{5}.\dfrac{9}{11}+\dfrac{5}{6}\)
b)\(2\dfrac{1}{2}.60\%-\left(\dfrac{3}{7}+0,15\right):\dfrac{3}{10}\)
c)\(15\dfrac{3}{13}-\left(3\dfrac{4}{7}+8\dfrac{3}{13}\right)\)
d)\(\dfrac{-7}{9}.\dfrac{4}{11}+\dfrac{-7}{9}.\dfrac{7}{11}+5\dfrac{7}{9}\)
e)\(50\%.1\dfrac{1}{3}.10.\dfrac{7}{35}.0,75\)
Tính
A = \(\dfrac{3}{2.5}\)+\(\dfrac{4}{5.6}\)+\(\dfrac{7}{6.13}\)+\(\dfrac{11}{13.24}\)
B=\(\dfrac{2}{3.4}\)+\(\dfrac{2}{4.9}\)+\(\dfrac{2}{5.6}\)\(\dfrac{2}{6.7}\)+\(\dfrac{2}{7.8}\)
so sánh
a,\(\dfrac{14}{21}và\dfrac{60}{72}\)
b,\(\dfrac{11}{54}và\dfrac{22}{37}\)
\(\dfrac{3}{4}\)+(\(\dfrac{1}{2}\)-5).\(\dfrac{2}{9}\)
Bài 1:
Tìm 2 số nguyên dương sao cho tích 2 số gấp 4 lần tổng 2 số
bài 2:Tìm a,b là 2 số tự nhiên biết:
\(\dfrac{a}{b}\)là phân số tối giản và \(\dfrac{a+b}{a^2+ab+b^2}\)=\(\dfrac{49}{1801}\)
bài 3: rút gọn
\(\dfrac{25^{28}+25^{24}+25^{20}+....+25^4+1}{25^{30}+25^{28}+25^{26}+....+25^2+1}\)
bài 4:cho x,y là các số nguyên chứng tỏ rằng 6x+11y chia hết cho 31 thì x+7y cũng chia hết cho 31
Tính:
\(\dfrac{2}{3}\)- \(\dfrac{5}{7}\). \(\dfrac{14}{25}\)
Tính nhanh :
Q = \(\left(\dfrac{1}{99}+\dfrac{12}{999}+\dfrac{123}{9999}\right).\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)
