\(\text{Bài 1 : Tính}\)
\(A=\frac{2^2\cdot10+2^3\cdot6}{2^2\cdot15-2^4}\)
\(B=\frac{2^9\cdot15^{17}\cdot75^3}{18^8\cdot5^{24}\cdot9^2}\)
\(C=\frac{7^{28}+7^{24}+...+7^4+7^0}{7^{30}+7^{28}+...+7^2+7^0}\)
Tính nhanh
A=\(\frac{1\cdot5\cdot6+2\cdot10\cdot12+3\cdot15\cdot18+4\cdot20\cdot24+5\cdot25\cdot30}{1\cdot3\cdot5+2\cdot6\cdot10+3\cdot9\cdot15+4\cdot12\cdot20+5\cdot15\cdot25}\)
A=1.5.(3.2)+2.10.(6.2)+3.15.(9.2)+4.20.(12.2)+5.25.(15.2)
1.3.5+2.6.10+3.9.15+4.12.20+5.15.25
A=1.5.3+2.10.6+3.15.9+4.20.12+5.25.15(2.2.2.2.2)
1.3.5+2.6.10+3.9.15+4.12.20+5.15.25
A=2.2.2.2.2
A=32
\(\frac{1\cdot3\cdot5\cdot2+2\cdot10\cdot6\cdot2+3\cdot15\cdot9\cdot2+4\cdot20\cdot12\cdot2+5\cdot25\cdot15\cdot2}{1\cdot3\cdot5+2\cdot10\cdot6+3\cdot15\cdot9+4\cdot20\cdot12+5\cdot25\cdot15 }\)
\(2\cdot2\cdot2\cdot2\cdot2=2^5\)
\(=32\)
làm bừa thui,ai trên 11 điểm tích mình mình tích lại
Số số hạng là :
Có số cặp là :
50 : 2 = 25 ( cặp )
Mỗi cặp có giá trị là :
99 - 97 = 2
Tổng dãy trên là :
25 x 2 = 50
Đáp số : 50
\(A=\frac{1.5\cdot6+2\cdot10\cdot12+3\cdot15\cdot18+4\cdot20\cdot24+5\cdot25\cdot30}{1\cdot3\cdot5+2\cdot6\cdot10+3\cdot9\cdot15+4\cdot12\cdot20+5\cdot15\cdot25}\)
=\(\frac{30\left(1+8+27+64+125\right)}{5\left(3+24+81+64+375\right)}\)
= \(\frac{30.225}{5.574}\)
=\(\frac{6750}{2870}\)
=\(\frac{675}{287}\)
K mình với!!!!
\(41\sqrt[9^1]{8\sqrt[2]{\frac{12}{2.85\frac{1\cdot2+3\cdot4+5\cdot6+7\cdot8+9\sqrt[4]{16}}{2\cdot\frac{12}{2}\sqrt{4^2}-7^2}}}4\cdot5\cdot6\cdot7\cdot8\cdot9}\)
Ô phép tính khủng. Cái này do bạn chế ra à !
\(\frac{7}{3\cdot4}-\frac{9}{4\cdot5}+\frac{11}{5\cdot6}-\frac{13}{6\cdot7}+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}+\frac{19}{9\cdot10}\)
ta có:(3+4)/4=3/(3*4)+4/(3*4) =1/4+1/3 chứng minh tương tự,cộng vế với vế, ta được kết quả là 13/30
Help me:
Tính:
( 2-1 + 3-1 ) : ( 2-1 - 3-1 ) + ( 2-1 : 20 ) :23
\(\frac{\left(\frac{2}{5}\right)^7\cdot5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7\cdot5^2+512}\)
\(\frac{4^6\cdot9^5+6^9\cdot120}{^{8^4\cdot3^{12}-6^{11}}}\)
\(\frac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
Rút gọn biểu thức sau: \(\frac{1\cdot3\cdot5+2\cdot6\cdot10+3\cdot9\cdot15}{3\cdot5\cdot12+6\cdot10\cdot24+9\cdot15\cdot36}\)
\(\frac{1\cdot3\cdot5+2\cdot6\cdot10+3\cdot9\cdot15}{3\cdot5\cdot12+6\cdot10\cdot24+9\cdot15\cdot36}=\frac{1+1+1}{12+12+12}=\frac{3\cdot1}{3\cdot12}=\frac{1}{12}\)
Tính
\(C=\frac{7^{28}+7^{24}+...+7^4+7^0}{7^{30}+7^{28}+...+7^2+7^0}\)
Ai nhanh 3 tick !
Cách tui lẹ hơn cách bạn Nguyễn Duy Khánh nè!
Ta có: \(C=\frac{7^{28}+7^{24}+....+7^4+7^0}{\left(7^{30}+7^{26}+...+7^6+7^2\right)+\left(7^{28}+7^{24}+...+7^4+7^0\right)}\)
\(=\frac{7^{28}+7^{24}+...+7^4+7^0}{7^2\left(7^{28}+7^{24}+...+7^4+7^0\right)+\left(7^{28}+7^{24}+...+7^4+7^0\right)}\)
\(=\frac{7^{28}+7^{24}+...+7^4+7^0}{\left(7^{28}+7^{24}+...+7^4+7^0\right)\left(7^2+1\right)}=\frac{1}{7^2+1}=\frac{1}{50}\)
P/s: Easy đúng không?
\(C=\frac{7^{28}+7^{2\text{4}}+...+7^{\text{4}}+7^0}{7^{30}+7^{28}+...+7^2+7^0}\)
Đặt A là tử số ,B là mẫu số.Ta có:
\(7^{\text{4}}A=7^{32}+7^{28}+...+7^8+7^{\text{4}}+7^0\)
\(20\text{4}1A-A=\left(7^{32}+7^{28}+7^{2\text{4}}+...+7^8+7^{\text{4}}\right)-\left(7^{28}+7^{2\text{4}}+...+7^{\text{4}}+7^0\right)\)
\(2\text{4}00A=7^{32}-7^0=7^{32}-1\)
\(\Rightarrow A=\left(7^{32}-1\right):2\text{4}00\)
\(7^2B=\left(7^{32}+7^{30}+7^{28}+...+7^{\text{4}}+7^2\right)\)
49B-B= ....tự..điền......như A nhé.....
48B=732-1 =>B=[7232-1]:48
=>\(C=\frac{A}{B}=\frac{\left(7^{32}-1\right):2\text{4}00}{\left(7^{32}-1\right):\text{4}8}\)
Tui nghĩ vậy đc r á
p/s:ko chắc
.
Đặt: \(A=7^{28}+7^{24}+...+7^4+7^0\)
=> \(7^4.A=7^{32}+7^{28}+...+7^8+7^4\)
=> \(7^4.A-A=\left(7^{32}+7^{28}+...+7^8+7^4\right)-\left(7^{28}+7^{24}+...+7^4+7^0\right)\)
=> \(\left(7^4-1\right).A=7^{32}-1\)
=> \(A=\frac{7^{32}-1}{7^4-1}\)
Đặt: \(B=7^{30}+7^{28}+...+7^2+7^0\)
tương tự tính được: \(B=\frac{7^{32}-1}{7^2-1}\)
\(C=\frac{A}{B}=\frac{7^{32}-1}{7^4-1}:\frac{7^{32}-1}{7^2-1}=\frac{7^2-1}{7^4-1}\)
\(=\frac{7^2-1}{\left(7^2-1\right)\left(7^2+1\right)}=\frac{1}{7^2+1}=\frac{1}{50}\)
\(a=\frac{2\cdot9\cdot8+3\cdot12\cdot10+4\cdot15\cdot12+...+98\cdot297\cdot200}{23\cdot4+3\cdot4\cdot5+4\cdot5\cdot6+...+98\cdot99\cdot100}\)
Tính a2
Tách phần lử trên ra sao cho có thể rút gọn với phần ơn dưới
Tính nhanh:
\(\frac{33}{2}+\frac{33}{6}+\frac{33}{18}+\frac{33}{54}+\frac{33}{162}+\frac{33}{486}\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)
\(\frac{33}{2}+\frac{33}{6}+\frac{33}{18}+\frac{33}{54}+\frac{33}{162}+\frac{33}{486}\)
\(=\frac{33.3+33.3+33.3+33.3+33.3}{486}\)
\(=\frac{99.5}{486}\)
\(=\frac{495}{486}\)
Gọi \(A=\frac{33}{2}+\frac{33}{6}+...+\frac{33}{486}\)
\(A=33.\left[\left(\frac{1}{1.2}+\frac{1}{2.3}\right)+\left(\frac{1}{3.6}+\frac{1}{6.9}\right)\left(\frac{1}{9.18}+\frac{1}{18.27}\right)\right]\)
\(A=33.\left[\frac{2}{3}+\frac{2}{9}+\frac{2}{27}\right]\)
\(A=66.\left[\frac{9}{27}+\frac{3}{27}+\frac{1}{27}\right]\)
\(A=66.\frac{13}{27}\)
\(A=\frac{286}{9}\)
sai hay đúng cx ko biết nha
\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(=1+\frac{2}{3}-\frac{2}{3}+\frac{2}{5}-\frac{2}{5}+....+\frac{2}{15}\)
\(=1+\frac{2}{15}\)
\(=\frac{17}{15}\)