Question

Calcule a soma dos 8 termos iniciais da PG (100 , 10 , 1 , 1/10 , ...)

Answer 1

$Sn = \frac{a1*(q^n-1)}{q-1} \\ Sn= \frac{100[( \frac{1}{10} )^8-1]}{ \frac{1}{10} -1} \\ Sn= \frac{100( \frac{1}{100000000}-1) }{ \frac{1-10}{10} } \\ Sn= \frac{100( \frac{1-100000000}{100000000}) }{ \frac{-9}{10} } \\ Sn= \frac{100( \frac{-99999999}{100000000}) }{ \frac{-9}{10} } \\ Sn= \frac{ \frac{-99999999}{1000000} }{ \frac{-9}{10} } \\ Sn= \frac{-99999999}{1000000} * (-\frac{9}{10} ) \\ \\ Sn = \frac{899999991}{10000000}$