Question

- uhmm tớ suy nghĩ quài mà không ra giúp tớ với nhé ^^

Câu 1: a. Chứng minh : 1/2 * [ (1/2n-1)-(1/2n+1) ] = 1/(2n-1)*(2n+1)

b.Tính : A=1/1*3 + 1/3*5 + 1/5*7 +.......+1/(2n-1)*(2n+1)

Câu 2 : Tìm a,b,c biết :

9x^2-16x+4/ x^3 - 3x^2+2x = a/x + b/x-1 + c/x-2

Answer 1

Câu 1:

a: \(=\dfrac{1}{2}\cdot\dfrac{2n+1-2n+1}{\left(2n-1\right)\left(2n+1\right)}=\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\)

b: \(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{\left(2n-1\right)\left(2n+1\right)}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2n-1}-\dfrac{1}{2n+1}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2n}{2n+1}=\dfrac{n}{2n+1}\)