Bài 1: Tính(hợp lý nếu có thể) e) \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\) f)\(\frac{12}{19}\cdot\frac{7}{15}\cdot\frac{-13}{17}\cdot\frac{19}{12}\cdot\frac{17}{13}\) g) \(\left(\frac{-4}{5}+\frac{4}{3}\right)+\left(\frac{-5}{4}+\frac{14}{5}\right)-\frac{7}{3}\)
chứng minh rằng:
A=\(\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{44}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}< \frac{1}{2}\)
Rút gọn phân số A = \(\dfrac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+....+25^2+1}\)
\(\text{Thực hiện phép tính một cách hợp lý nhất (nếu có thể):}\)
\(1\)) \(\left(\dfrac{-8}{13}:\dfrac{3}{7}+\dfrac{-5}{13}:\dfrac{3}{7}\right).\dfrac{\left(-4\right)^3.\left|-3\right|}{7}\)
\(2\)) \(75\)\(\text{%}\)\(-\left(\dfrac{5}{2}+\dfrac{5}{3}\right)+\left(-\dfrac{1}{2}\right)^2\)
a)Rút gọn phân số : \(\dfrac{25^{28}+25^{24}+25^{20}+.....+25^4+1}{25^{30}+25^{28}+....+25^2+1}\)
b) Cho S = 1-3 + 32-33+.....+398-399
thực hiện các phép tính sau:
A =\(\frac{5.2^{30}.3^{18}-4.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
B = 1 - 3 + 5 - 7 + 9 - 11 + ..... + 2017 - 2019
C =\(\left(\frac{151515}{606060}+\frac{151515}{121212}+\frac{151515}{202020}+\frac{151515}{303030}+\frac{151515}{424242}\right).\frac{28}{15}\)
Bài 1: Tính hợp lý (nếu có thể)
a) (-193)+36+14+193
b) 2008-(127+2008)+(-35+127)
c) (273-28)+(129-72)
d) 21×35-5×11×7
e) (-13)×34-87×34
f) 85×(35-27)-35×(85-27)
g) 1-2-3+4+5-6-7+…+97-98-99+100
h) 2100-299-298-…-22-2-1
Tính A=2528 +2524+2520+...+254+1/2530 +2528+2526+...+252+1
Cho P=\(\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{41}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}\)
Chứng minh rằng P<1/2