Ôn tập toán 8
Các câu hỏi tương tự
Tính A = \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{97.99}\right)+\left(-2-4-6-...-100\right)+\)\(\left(-1.2-2.3-3.4-...-99.100\right)\)
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
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:
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
Chứng minh rằng với mọi số nguyên dương n, ta có:
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{n\left(n+1\right)\left(n+2\right)}< \frac{1}{4}\)
Tìm x :a) \(\frac{x-214}{86}+\frac{x-132}{84}+\frac{x-54}{82}+\frac{x-20}{80}=10\)
b) \(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\left(-3,2\right)+\frac{2}{5}\right|\)
c) \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
Tìm x : \(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{6}\right|+\left|x+\frac{1}{12}\right|+\left|x+\frac{1}{20}\right|+...+\left|x+\frac{1}{110}\right|=11x\)
Tìm x : \(\frac{2\left(x-1\right)\left(x-3\right)}{3}-\frac{4\left(2x-1\right)^2}{5}=\frac{\left(1+3x\right)^2}{2}-3x\left(1-x\right)\)
Tìm x : \(\frac{2\left(x-1\right)\left(x-3\right)}{3}-\frac{4\left(2x-1\right)^2}{5}=\frac{\left(1+3x\right)^2}{2}-3x\left(1-x\right)\)