## Multivariable Calculus, 7th Edition

$S_{y}= 16$
The values in the sequence are getting smaller and smaller in a geometric sequence. When we divide consecutive terms, we see we have a common ratio of 3/4. We can use the formula $S_{y}=a/(1-r)$, where a is the first term and r is the ratio between terms. Thus: $S_{y}=4/(1-3/4)=4/(1/4)=16$