1) Theo tinh chat phan thuc thi 2 phan thuc nao sau day bang nhau
A. \(\dfrac{5x^3y^4}{6xy^2}\) va \(\dfrac{10x^4y^2}{12x^2}\)
B. \(\dfrac{5x^3y^4}{6xy^2}\) va \(\dfrac{10x^3y^2}{12x^2}\)
C. \(\dfrac{5x^3y^4}{6xy^2}\) va \(\dfrac{10x^3y^2}{12x}\)
D. \(\dfrac{5x^3y^4}{6xy^2}\) va \(\dfrac{10x^3y^2}{12x^2y}\)
1) Dieu kien cua x de phan thuc \(\dfrac{2x^3y^5}{5\left(x-2\right)^2}\) co nghia la
A. x ≠ 2 B. x ≠ -2
C. x = -2 D. x = 2
1) Ket qua quy dong mau thuc cua 2 phan thuc \(\dfrac{1}{x-1}\) va \(\dfrac{2}{x+1}\) la:
1) Thuc hien phep tinh cong 2 phan thuc \(\dfrac{2x}{x^2-2x+1}+\dfrac{x+1}{x-1}\) duoc ket qua la:
A. \(\dfrac{x^2+2x+1}{\left(x-1\right)^2}\) B. \(\dfrac{x^2+2x-1}{\left(x-1\right)^2}\) C. \(\dfrac{x^2-x-1}{\left(x-1\right)^2}\) D. \(\dfrac{x^2-2x-1}{\left(x-1\right)^2}\)
1) Ket qua khi rut gon phan thuc \(\dfrac{x^2+2x+1}{x^3+1}\) la:
Chứng minh rằng với \(n\in N^{\circledast}\), ta có các đẳng thức :
a) \(2+5+8+.....+3n-1=\dfrac{n\left(3n+1\right)}{2}\)
b) \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+....+\dfrac{1}{2^n}=\dfrac{2^n-1}{2^n}\)
c) \(1^2+2^2+3^2+....+n^2=\dfrac{n\left(n+1\right)\left(2n+1\right)}{6}\)
1) Tai sao \(\dfrac{1}{2^{k+1}}=\dfrac{1}{2^k.2}\)
Chứng minh các đẳng thức sau (với \(n\in N^{\circledast}\) )
a) \(1^2+3^2+5^2+.....+\left(2n-1\right)^2=\dfrac{n\left(4n^2-1\right)}{3}\)
b) \(1^3+2^3+3^3+.....+n^3=\dfrac{n^2\left(n+1\right)^2}{4}\)
Chứng minh bằng phương pháp quy nạp toán học: \(\forall n\in N\)*, n>1; ta có: \(\dfrac{1}{n+1}+\dfrac{1}{n+2}+...+\dfrac{1}{2n}>\dfrac{13}{24}\)
Chứng minh các đẳng thức sau (với \(n\in N^{\circledast}\))
a) \(2+5+8+...+\left(3n-1\right)=\dfrac{n\left(3n+1\right)}{2}\)
b) \(3+9+27+....+3^n=\dfrac{1}{2}\left(3^{n+1}-3\right)\)
