Final answer:
To find limits of sequences, simplify algebra by eliminating terms and use series expansions like the Binomial theorem. Always ensure to check the result to confirm its reasonableness.
Step-by-step explanation:
To solve limits of sequences, a specific problem-solving strategy can be followed. This includes a series of steps starting from identifying knowns and unknowns to checking if the answer is reasonable. For instance, when faced with a sequence limit problem, you should eliminate terms wherever possible to simplify the algebra involved.
After solving the limit, ensure to check the answer against the original problem to see if it makes sense in the context. This process not only helps in obtaining the correct answer but also assists in solidifying knowledge about the behavior of the sequence as it approaches a certain term number or infinity.
Applying series expansions can offer further help in finding limits of sequences, where common expansions like the Binomial theorem could potentially simplify complex terms within the sequence. For example, using the Binomial theorem expansion for (a + b) to a sequence like (1/n + 1)^n could reveal a limit as n approaches infinity.