Find the sum of the infinite series
\[
-1+\frac{7}{10}\cdot 2^2-\frac{7\cdot 9}{10\cdot 15}\cdot 2^3+\frac{7\cdot 9\cdot 11}{10\cdot 15\cdot 20}\cdot 2^4-\cdots\infty
\]
Show Hint
In infinite series involving products like \(7\cdot9\cdot11\cdots\), first rewrite the coefficients in factorial form and compare them with the standard binomial expansion of \((1+x)^{-n}\).