Question

If $(1 - x + x^{2} - x^{3} + x^{4} - ..)\left( 1 + \frac{x}{2} + \left( \frac{x}{2} \right)^{2} + \left( \frac{x}{2} \right)^{3} + ... \right)$then $x^{4}$

• A. 5
• B. $\frac{x^{2} + 1}{(x^{2} + 4)(x - 2)} = \frac{Ax + B}{x^{2} + 4} + \frac{C}{x - 2}$
• C. $\Rightarrow$
• D. $x^{2} + 1 = (Ax + B)(x - 2) + C(x^{2} + 4)$

Answer 1

Answer: (D)

$x^{2} + 1 = (Ax + B)(x - 2) + C(x^{2} + 4)$

Answer 2

$\sum_{n = 1}^{n}\frac{1}{\log_{2^{n}}(a)} = \sum_{n = 1}^{n}{\log_{a}2^{n}}$

$x = 1$

$\log_{a}2.\frac{n(n + 1)}{2} = \frac{n(n + 1)}{2}\log_{a}2$= $\log_{7}{\log_{5}(}\sqrt{x^{2} + 5 + x}) = 0 = \log_{7}1$;

$\Rightarrow$ $134 + \sqrt{6292} = \lbrack 11^{2} + (\sqrt{13})^{2}\rbrack + 2.11.\sqrt{13}$

$\Rightarrow$

$(x^{2} + 5 + x)^{1/2} = 5 \Rightarrow$; $(x^{2} + x + 5) = 25 \Rightarrow$.