Question

True or false? If P(n) is a summation formula for the sigma sum LaTeX: \sum_{k=0}^n f(k) =S(n)∑ k = 0 n f ( k ) = S ( n ) , where S(n) represents the sum in closed form, we prove the statement P(n+1) from P(n) by taking the statement P(n) and adding f(n+1) to both sides. Then we simplify S(n)+f(n+1) algebraically to show that it is S(n+1).

Answer 1

True

Explanation:

Based on the expression provided in the question, it can be the statement P(n+1) can be derived from the statement P(n) by the addition of f(n+1) to both sides of the statement P(n). Furthermore, the expression S(n)+f(n+1) can be simplified algebraically to derive an expression S(n+1). Therefore, the above sentence is true.