Question

[Hoàng Thảo Linh]

1.rút gọn biểu thức

\(A=\dfrac{1^2}{2^2-1}.\dfrac{3^2}{4^2-1}.\dfrac{5^2}{6^2-1}......\dfrac{n^2}{\left(n+1\right)^2-1}\)

2. rút gọn biểu thức

\(B=\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)

3. rút gọn biểu thức

\(C=\dfrac{3}{\left(1.2\right)^2}+\dfrac{5}{\left(2.3\right)^2}+......+\dfrac{2n+1}{[n\left(n+1\right)]^2}\)

4. cho a + b + c = 0 và (a.b.c khác 0)

rút gọn : \(D=\dfrac{ab}{a^2+b^2-c^2}+\dfrac{bc}{b^2+c^2-a^2}+\dfrac{ca}{c^2+a^2-b^2}\)

giúp mk vs

Answer 1

[tui là mọt sách @~@]

A= \(\dfrac{1^2}{\left(2-1\right)\left(2+1\right)}\cdot\dfrac{3^2}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{n^2}{n\left(n+2\right)}\)

= \(\dfrac{1}{1\cdot3}\cdot\dfrac{3^2}{3\cdot5}\cdot\dfrac{5^2}{5\cdot7}\cdot...\cdot\dfrac{n^2}{n\left(n+2\right)}\)

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

Answer 2

[tui là mọt sách @~@]

B = \(\dfrac{1+x+1-x}{\left(1-x\right)\left(1+x\right)}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)

= \(\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)

= \(\dfrac{4}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)

= \(\dfrac{8}{1-x^8}+\dfrac{8}{1+x^8}=\dfrac{16}{1-x^{16}}\)