Question

3/(1-а^3)+3/(1+а^3)+6/(1+а^6)+12/(1+а^12)+24/(1+а^24)+48/(1+а^48)=?

Answer 1

$\displaystyle\frac{3}{1-a^3}+\frac{3}{1+a^3} +\frac{6}{1+a^6}+\frac{12}{1+a^{12}}+\frac{24}{1+a^{24}}+\frac{48}{1+a^{48}}=\\ \\ \\ =\frac{6}{1-a^6} +\frac{6}{1+a^6}+\frac{12}{1+a^{12}}+\frac{24}{1+a^{24}}+\frac{48}{1+a^{48}}=\\ \\ \\ =\frac{12}{1-a^{12}}+ \frac{12}{1+a^{12}}+\frac{24}{1+a^{24}}+\frac{48}{1+a^{48}}=\\ \\ =\frac{24}{1-a^{24}}+ \frac{24}{1+a^{24}}+\frac{48}{1+a^{48}}=\frac{48}{1-a^{48}} +\frac{48}{1+a^{48}}=\frac{96}{1-a^{96}}$

Answer 2

To find the value of the given expression, let's start by combining the fractions with a common denominator. The common denominator in this case is (1 - а^3)(1 + а^3)(1 + а^6)(1 + а^12)(1 + а^24)(1 + а^48). After combining the fractions, we can simplify the expression. However, it is important to note that the value of 'а' is not provided in the question. Without knowing the value of 'а,' we cannot evaluate the expression.

The simplified expression is as follows:

(3 * (1 + а^3)(1 + а^6)(1 + а^12)(1 + а^24)(1 + а^48) + 3 * (1 - а^3)(1 + а^6)(1 + а^12)(1 + а^24)(1 + а^48) + 6 * (1 - а^3)(1 + а^3)(1 + а^12)(1 + а^24)(1 + а^48) + 12 * (1 - а^3)(1 + а^3)(1 + а^6)(1 + а^24)(1 + а^48) + 24 * (1 - а^3)(1 + а^3)(1 + а^6)(1 + а^12)(1 + а^48) + 48 * (1 - а^3)(1 + а^3)(1 + а^6)(1 + а^12)(1 + а^24)) / ((1 - а^3)(1 + а^3)(1 + а^6)(1 + а^12)(1 + а^24)(1 + а^48))

Again, without the value of 'а,' we cannot proceed to calculate the exact result of the expression. If you provide the value of 'а,' I'd be happy to help you find the result.