Hello,
[tex]s=2-3+ \dfrac{9}{2} - \dfrac{27}{4} +...- \dfrac{177147}{1024} \\\\
=2(1- \dfrac{3}{2} + \dfrac{3^2}{2^2} - \dfrac{3^3}{2^3}+...- \dfrac{3^{11}}{2^{11}} )\\\\
=2( \dfrac{1- (\dfrac{-3}{2})^{12}}{1+ \dfrac{3}{2} } )\\\\
=2( \dfrac{2^{12}-3^{12}}{ \dfrac{5}{2} } )\\\\
= \dfrac{4}{5*4096} *(-527345)=-102,9970703125[/tex]
