Ыыы хелп. S₅ = 1 * (-√2)⁵ - 1) / -√2 - 1

Решите задачу:

$S_{5}= \frac{1*( (- \sqrt{2} )^{5}-1) }{- \sqrt{2} -1} = \frac{- \sqrt{ 2^{4}*2 }-1 }{- \sqrt{2} -1}= \frac{-( 2^{2} \sqrt{2} +1)}{-( \sqrt{2} +1)} = \frac{4 \sqrt{2}+1 }{ \sqrt{2} +1} = \frac{(4 \sqrt{2} +1)*( \sqrt{2} -1)}{( \sqrt{2} +1)*( \sqrt{2} -1)}$ $\frac{4 \sqrt{ 2^{2} } + \sqrt{2} -4 \sqrt{2} -1}{ \sqrt{ 2^{2} } - 1^{2} } = \frac{4*2-3 \sqrt{2} -1}{2-1}= \frac{8-1-3 \sqrt{2} }{1} =7-3 \sqrt{2}$