Question

Вычислите:

(5+1)(5^2+1)(5^4+1)(5^8+1)*...*(5^1024+1)-0,25*5^2048

Answer 1

$\sf (5+1)(5^2+1)< \cdot \cdot \cdot >(5^{1024}+1)-0.25\cdot5^{2048}= \\ =\dfrac{(5-1)(5+1)(5^2+1)< \cdot \cdot \cdot >(5^{1024}+1)}{4}-\dfrac{1}{4}\cdot5^{2048}= \\ =\dfrac{1}{4}(5^{2048}-1)-\dfrac{1}{4}\cdot5^{2048}=\boxed{\sf-\dfrac{1}{4}}$