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When the degree of the numerator is strictly greater than the degree of the denominator in a rational function, the function grows without bound as the variable approaches infinity. Consequently, the limit is infinity.

Conditions: The function is a quotient of two polynomials.; The degree of the numerator is greater than the degree of the denominator.; The variable approaches infinity.

When the degree of the numerator is strictly greater than the degree of the denominator in a rational function, the function grows without bound as the variable approaches infinity. Consequently, the limit is infinity.

Conditions: The function is a quotient of two polynomials.; The degree of the numerator is greater than the degree of the denominator.; The variable approaches infinity.

To determine if an infinite series converges or diverges when given an explicit formula for its $n$-th partial sum $S_n$, evaluate the limit $\lim_{n \to \infty} S_n$. If this limit exists and is a finite value, the series converges to that value; if the limit is infinite or does not exist, the series diverges.

Conditions: You are given an explicit algebraic formula for the $n$-th partial sum, $S_n$.; The limit is taken as $n \to \infty$.

To determine if an infinite series converges or diverges when given an explicit formula for its $n$-th partial sum $S_n$, evaluate the limit $\lim_{n \to \infty} S_n$. If this limit exists and is a finite value, the series converges to that value; if the limit is infinite or does not exist, the series diverges.

Conditions: You are given an explicit algebraic formula for the $n$-th partial sum, $S_n$.; The limit is taken as $n \to \infty$.