rút gọn:
a)\(\frac{4^3.1^5}{9^2.8^2}\) b)\(\frac{25^2.2^2.4^1}{3^3.2^3.224}\) c)\(\frac{25^3.5^6.5^2}{9^4.10^2}\)
a,\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
b,\(\frac{27^2.8^5}{6^6.32^3}+\frac{3^4.4^4}{2^2.6^2}\)
c,\(\left(1+\frac{1}{1.3}\right)\)\(\left(1+\frac{1}{2.4}\right)\)\(\left(1+\frac{1}{3.5}\right)\)........\(\left(1+\frac{1}{20.22}\right)\)
d,\(\frac{3}{2}\)+\(\frac{7}{6}\)+\(\frac{13}{12}+\frac{21}{20}+.....+\frac{91}{90}\)
e,\(\left(-2^2\right)+\sqrt{36}-\sqrt{9}+\sqrt{25}\) 20).20)
tính:a.\(2^6.5^6\)b.\(8^2.5^2\)c.\(4^3.5^3\)d.\(5^2.6^2.3^2\)e.\(\frac{625^5}{25^8}\)g.\(\frac{3^9}{7}.\frac{7^9}{3}\)
giúp mình nha các bạn !
a , 106 b , 402 c 203 d,902 e , 54 g , 218
#)Giải :
a)\(2^6.5^6=\left(2.5\right)^6=10^6\)
b)\(8^2.5^2=\left(8.5\right)^2=40^2\)
c)\(4^3.5^3=\left(4.5\right)^3=20^3\)
d)\(5^2.6^2.3^2=\left(5.6.2\right)^2=60^2\)
e)\(\frac{625^5}{25^8}=\frac{\left(25^2\right)^5}{25^8}=\frac{25^{10}}{25^8}=25^2\)
g)\(\frac{3^9}{7}.\frac{7^9}{3}=\frac{\left(3.7\right)^9}{7.3}=\frac{21^9}{21}=21^8\)
a) 26 . 56 = (2.5)6 = 106
b) 82.52 = (8.5)2 = 402
c) 43.53 = (4.5)3 = 203
d) 52.62.32 = (5.6.2)2 = 602
e) \(\frac{625^5}{25^8}=\frac{\left(25^2\right)^5}{25^8}=\frac{25^{2.5}}{25^8}=\frac{25^{10}}{25^8}=\frac{25^8.25^2}{25^8}=25^2=625\)
g) \(\frac{3^9}{7}.\frac{7^9}{3}=\frac{3^9.7^9}{7.3}=\frac{\left(7.3\right)^9}{7.3}=\frac{21^9}{21}=21^8\)
Tính nhanh
a ) \(\frac{5}{7}.\frac{5}{11}+\frac{5}{7}.\frac{2}{11}-\frac{5}{7}.\frac{10}{11}\)
b) \(\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}.\frac{25}{4.6}.\frac{36}{5.7}\)
c) \(6\frac{4}{11}+\frac{8}{72}-\left(3\frac{8}{22}+\frac{1}{9}\right)\)
Thực hiện phép tính:
a) \(\frac{-5}{9}.\left(\frac{3}{10}-\frac{2}{5}\right)\)
b) \(2^8:2^5+3^3.2-12\)
c) \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+1^{2012}\)
d) \(\left(-3\right)^2+\sqrt{\frac{16}{25}}-\sqrt{9}+\frac{\sqrt{81}}{3}\)
\(a,\frac{-5}{9}.\left(\frac{3}{10}-\frac{2}{5}\right)\)
\(=\frac{-5}{9}.\frac{-1}{10}\)
\(=\frac{1}{18}\)
\(b,2^8:2^5+3^3.2-12\)
\(=2^3+9.2-12\)
\(=8+18-12\)
\(=26-12\)
\(=14\)
Câu c,d em chưa học nên không biết làm ạ, mong mọi người thông cảm!!!
Sửa lại câu b
\(=2^3+27.2-12\)
\(=8+54-12\)
\(=62-12\)
\(=50\)
Chứng minh rằng: \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+....................+\frac{19}{9^2.10^2}< 1\)
Đặt \(A=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)
\(\Rightarrow A=\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+\frac{4^2-3^2}{3^2.4^2}+...+\frac{10^2-9^2}{9^2.10^2}\)
\(\Rightarrow A=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+\frac{1}{3^2}-\frac{1}{4^2}+...+\frac{1}{9^2}-\frac{1}{10^2}\)
\(\Rightarrow A=\frac{1}{1^2}-\frac{1}{10^2}\)
\(\Rightarrow A=1-\frac{1}{10^2}\)
Mà \(1-\frac{1}{10^2}< 1.\)
\(\Rightarrow A< 1\left(đpcm\right).\)
Chúc bạn học tốt!
Chứng minh rằng:
\(\frac{3}{1^2.2^2}+\frac{5}{2^2.4^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}<1\)
\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)
\(=\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+\frac{4^2-3^2}{3^2.4^2}+....+\frac{10^2-9^2}{9^2.10^2}\)
\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+\frac{1}{3^2}-\frac{1}{4^2}+....+\frac{1}{9^2}-\frac{1}{10^2}=\frac{1}{1^2}-\frac{1}{10^2}<1\)
=>đpcm
chứng minh rằng:
a) A= \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)<1
b)B=\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{4^4}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
\(A=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+....+\frac{19}{9^2.10^2}\)
\(A=\frac{3}{1.4}+\frac{5}{4.9}+\frac{7}{9.16}+....+\frac{19}{81.100}\)
\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+....+\frac{1}{81}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}< 1\)
\(\Rightarrow A< 1\text{(đpcm) }\)
bài 1:
Cho A= \(\frac{3}{1^2.2^2}\)+ \(\frac{5}{2^2.3^2}\)+ \(\frac{7}{3^2.4^2}\)+.........+ \(\frac{9}{9^2.10^2}\) . So sánh A với 1
Bài 2:
Tìm tổng A= 1 - 7 + 13- 19 + 25 - 31+....... với A có n số hạng
A<1
bạn tính phần mẫu ra rồi làm như dạng sai phân bình thường
bài 1:
Cho A= \(\frac{3}{1^2.2^2}\)+ \(\frac{5}{2^2.3^2}\)+ \(\frac{7}{3^2.4^2}\)+.........+ \(\frac{9}{9^2.10^2}\) . So sánh A với 1
Bài 2:
Tìm tổng A= 1 - 7 + 13- 19 + 25 - 31+....... với A có n số hạng
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