Final answer:
The correct technique for simplifying the sum of square roots like √(n+1) - √n is a telescoping series, which allows for canceling out terms to simplify the expression effectively.
Step-by-step explanation:
When you have a sum of square roots such as √(n+1) - √n, the technique to use is known as telescoping series. This method involves taking a sequence of partial sums whose terms cancel each other out in a specific way to leave behind a simpler form. Telescoping sequences are particularly useful when dealing with the sum of square roots as they allow for the simplification of the expression by pairing terms such that many of them cancel out, leaving a much simpler result.
For this kind of problem, neither factorization, geometric series, nor Taylor series are the correct approach. While Taylor series might deal with expansions involving square roots, they are generally used for approximating functions and are not particularly useful for simplification in the same way as telescoping series for this type of problem.