Question

evaluate 22^8/(1+3+5+7+9+...............239+241)^2​

Answer 1

             

$\Rightarrow\ \boxed{\frac{22^8}{(1+3+5+......+241)^2}} \\ \\ \\ \Rightarrow\ \boxed{\frac{22^8}{(1+3+5+......+(2 \times 121-1))^2}} \\ \\ \\ \Rightarrow\ \boxed{\frac{22^8}{(121^2)^2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{\because\ 1+3+5+...+(2n-1)=n^2} \\ \\ \\ \Rightarrow\ \boxed{\frac{(11 \times 2)^8}{121^{2 \times 2}}} \\ \\ \\ \Rightarrow\ \boxed{\frac{11^8 \times 2^8}{121^4}} \\ \\ \\ \Rightarrow\ \boxed{\frac{11^8 \times 2^8}{(11^2)^4}} \\ \\ \\ \Rightarrow\ \boxed{\frac{22^8}{11^{2 \times 4}}}$

$\Rightarrow\ \boxed{\frac{11^8 \times 2^8}{11^8}} \\ \\ \\ \Rightarrow\ \boxed{2^8} \\ \\ \\ \Rightarrow\ \boxed{\bold{256}}$

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