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).

Question

Mathematics

Happy

8 September, 20:30

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).

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Moses Sharp · Answer 1

True

Step-by-step 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.