Ôn tập toán 8
Các câu hỏi tương tự
Tìm x : \(\left(1.2.3+2.3.4+...+2015.2016.2017\right)-\left(5.6+6.7+...+99.100\right)\) \(=\left(5+10+15+...+2000\right)-\frac{1}{1.3}-\frac{1}{3.5}-...-\frac{1}{97.99}-4x\)
TÌm x: ( 1.2.3 + 2.3.4 + ... + 20.21.22 ) - 5 - 7 - 9 - ... - 55 - 3x = \(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\right)-\frac{5}{1.3}-\frac{5}{3.5}-...-\frac{5}{53.55}-\) 8.9 - 9.10 - ... - 20.21
Rút gọn C = \(\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+...+\frac{2n+1}{\left[n\left(n+1\right)\right]^2}\)
a) Tính \(S=\left(-\frac{1}{7}\right)^0+\left(-\frac{1}{7}\right)^1+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2017}\)
b) So \(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}\) với \(1\)
Tính A=\(\frac{\left(1^4+\frac{1}{4}\right)\left(3^4+\frac{1}{4}\right)\left(5^4+\frac{1}{4}\right)...\left(11^4+\frac{1}{4}\right)}{\frac{\left(2^4+\frac{1}{4}\right)\left(4^4+\frac{1}{4}\right)\left(6^4+\frac{1}{4}\right)...\left(12^4+\frac{1}{4}\right)}{ }}\)
Tìm x :
a) \(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{103.105}\right).\left(x-1\right)=\frac{3}{5}x-\frac{7}{15}\)
b) \(\left(\frac{1}{1.101}+\frac{1}{2.102}+\frac{1}{3.103}+...+\frac{1}{10.110}\right)x=\frac{1}{1.11}+\frac{1}{2.12}+...+\frac{1}{100.110}\)
Tính \(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+\text{4}\right)+...+\frac{1}{2016}\left(1+2+...+2016\right)\)
a) Tìm x,y biết: x4+x2-y2+y+10=0
b) Tính giá trị biểu thức: \(\frac{\left(1+\frac{1}{4}\right)\left(3^4+\frac{1}{4}\right)\left(5^4+\frac{1}{4}\right)...\left(29^4+\frac{1}{4}\right)}{\left(2^4+\frac{1}{4}\right)\left(4^4+\frac{1}{4}\right)\left(6^4+\frac{1}{4}\right)...\left(30^4+\frac{1}{4}\right)}\)
1. Cho \(\frac{a}{c}=\frac{c}{b}\) Chứng minh \(\frac{a^2+c^2}{b^2+c^2}=\frac{a}{b}\)
2. Tính B = \(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6-8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)