Question If the following sequence converges, find its limit. If the sequence diverges, enter \( \varnothing \). \[ 7+\frac{2}{n^{4}} \]

As \( n \) approaches infinity, the term \( \frac{2}{n^{4}} \) approaches 0 because the denominator grows very large, making the fraction itself vanish. Therefore, the sequence simplifies to \( 7 + 0 = 7 \). Thus, the limit of the sequence is 7! To put it simply, as you keep plugging in larger numbers for \( n \), the added fraction becomes less and less significant, leading the entire expression to settle firmly at 7. It's like a party where the noise fades away, and you can distinctively hear the host's voice saying “7!”