Prove that : \(A=\dfrac{1}{3^2}+\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{n^2}< \dfrac{1}{4}\) ( n odd and n is greater than or equal to 3 )

For a + b + c = 0 . Prove that : \(a^3+b^3+c^3=0\)

1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 +5 x 6 + ... + 99 x 100 = 0

Find x :

Polynomial Analysis into Factors :

a ,  \(x^8+14x^4+1\)

b , \(x^8+98x^4+1\)

Prove that :

\(\dfrac{40^4+51^4+91^4}{79^4}=\dfrac{40^2+51^2+91^2}{79^2}\)

Compact expression :

\(B=\left(ab+bc+ca\right)\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)-abc\left(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}\right)\)