\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2n+1\right).\left(2n+3\right)}\)

= \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{\left(2n+1\right)}-\frac{1}{\left(2n+3\right)}\)

= \(1-\frac{1}{\left(2n+3\right)}\)

cách làm này ko biết sai hay đúng nên hãy cẩn thận

hơi khó bn ơi

kết quả cuối cùng tự tính nhé

a) Đặt B= 1/1.3 + 1/3.5 + 1/5.7 + .....+ 1/19.21

Ta có: 2B= 2/1.3 + 2/3.5 + 2/5.7 + ....+ 2/19.21

= 1- 1/3 + 1/3-1/5 + 1/5-1/7 +....+ 1/19-1/21

= 1-1/21 = 20/21

=> B= 20/21 : 2 => B= 10/21

b) Như trên, ta có: 2A= 1- (1/2n + 1) => A=( 1-1/2n+1).1/2

=> A= 1/2- 1/2n+1

=> A< 1/2 ( đpcm )

\(P=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{\left(2n+1\right)\left(2n+3\right)}\\ 2P=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{\left(2n+1\right)\left(2n+3\right)}\\ =\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2n+1}-\dfrac{1}{2n+3}\\ =1-\dfrac{1}{2n+3}\\ =\dfrac{2\left(n+1\right)}{2n+3}\\ P=\dfrac{2\left(n+1\right)}{2n+3}:2\\ =\dfrac{n+1}{2n+3}\)

Đặt A = 1/1.3 + 1/3.5 + 1/5.7 +........+ 1/(2n - 1)(2n + 1)
2.A = 2/1.3 + 2/3.5 + 2/5.7 +........+ 2/(2n - 1)(2n + 1)
2.A = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/(2n - 1) - 1/(2n + 1)
2.A = 1 - 1/(2n + 1) = 2n/(2n + 1)
Vậy A = n/(2n + 1)

1.3+3.5+5.7+...+(2n+1).(2n+3)=(2n+1).(2n+2).(2n+3).(2n+4)

(2n+2)(2n+2)(2n+3)(2n+4):12]+(n+1)

\(S=\frac{1.3}{3.5}+\frac{2.4}{5.7}+\frac{3.5}{7.9}+...+\frac{\left(n-1\right)\left(n+1\right)}{\left(2n-1\right)\left(2n+1\right)}+...+\frac{1002.1004}{2005.2007}\)

\(\Rightarrow S=\frac{\left(2-1\right)\left(2+1\right)}{\left(2.2-1\right)\left(2.2+1\right)}+\frac{\left(3-1\right)\left(3+1\right)}{\left(3.2-1\right)\left(3.2+1\right)}+...+\frac{\left(n-1\right)\left(n+1\right)}{\left(2n-1\right)\left(2n+1\right)}\)

\(+..+\frac{\left(1003-1\right)\left(1003+1\right)}{\left(1003.2-1\right)\left(1003.2+1\right)}\)

\(\Rightarrow S=\frac{1}{4}-\frac{3}{8}\left(\frac{1}{2.2-1}-\frac{1}{2.2+1}\right)+\frac{1}{4}-\frac{3}{8}\left(\frac{1}{3.2-1}-\frac{1}{3.2+1}\right)+...\)

\(+\frac{1}{4}-\frac{3}{8}\left(\frac{1}{2n-1}-\frac{1}{2n+1}\right)+...+\frac{1}{4}-\frac{3}{8}\left(\frac{1}{1003.2-1}-\frac{1}{1003.2+1}\right)\)

\(\Rightarrow S=1002.\frac{1}{4}-1002.\frac{3}{8}\left(\frac{1}{2.2-1}-\frac{1}{2.2+1}+\frac{1}{3.2-1}-...-\frac{1}{1003.2+1}\right)\)

\(\Rightarrow S=\frac{501}{2}-\frac{1503}{4}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2005}-\frac{1}{2007}\right)\)

\(\Rightarrow S=\frac{501}{2}-\frac{1503}{4}\left(\frac{1}{3}-\frac{1}{2007}\right)\)

\(\Rightarrow S=\frac{501}{2}-\frac{1503}{4}.\frac{668}{2007}\)

\(\Rightarrow S=\frac{501}{2}-\frac{27889}{223}\)

\(\Rightarrow S=125,4372197\)

\(\)

thx  you

1/ Ta có:

\(a^5-a^3+a=2\)

Dễ thấy a = 0 không phải là nghiệm từ đó ta có:

\(a^6-a^4+a^2=2a\)

\(\Rightarrow2a=a^6+a^2-a^4\ge2a^4-a^4\ge a^4\)

\(\Rightarrow\hept{\begin{cases}2a\ge a^4\\a>0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}2\ge a^3\\a>0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}4\ge a^6\\a>0\end{cases}}\)

Dấu = không xảy ra 

Vậy \(a^6< 4\)

Câu 2/

Câu hỏi của XPer Miner - Toán lớp 9 - Học toán với OnlineMath

Bạn tham khảo cách làm của bạn Alibabba nguyễn nha!!