Question

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

Answer 1

$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}$