Question

Find The sun of 2-3+9/2-27/4+.....-177147/1024

Answer 1

Hello,

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