The Maclaurin series for f(x)=ex\displaystyle {f{{\left({x}\right)}}}={e}^{{{x}}} is `
\sum_(n=0)^\infty (x)^n/(n!) =1+x+x^2/(2!)+x^3/(3!)+...`

By transforming the series for ex\displaystyle {e}^{{x}}, find the Maclaurin series for 7e4x\displaystyle {7}{e}^{{-{4}{x}}}.



+ + + + + ...


         

Written compactly, this series is

 n=0\displaystyle {\sum_{{{n}={0}}}^{{\infty}}}