Compute each sum below. Give exact values, not decimal approximations. If the sum does not exist, click on "No sum". \[ 5+5(3)+5(3)^{2}+\ldots=\square \]

To compute the sum \( S = 5 + 5(3) + 5(3)^{2} + \ldots \), we can first factor out the common factor of \( 5 \): \[ S = 5(1 + 3 + 3^{2} + \ldots) \] Now, we identify the series inside the parentheses. This is a geometric series with the first term \( a = 1 \) and common ratio \( r = 3 \). A geometric series converges if \( |r| < 1 \). In this case, \( |3| = 3 \) which is greater than 1, so the series diverges. Thus, the original sum does not exist: \[ \text{No sum} \]