Question

Summation simplification calculator

a) n(n + 1)/2
b) n(n - 1)/2
c) n² + n
d) n² - n

Answer 1

This is a mathematical problem about series and sequence summation, where manipulating the terms of a specific patterned series can simplify the sum to
`2n²` demonstrating the technique of summation simplification.

Step-by-step explanation:

The question is asking to simplify a series to find its sum. Specifically there's a reference to simplifying a series where each term increases in a specific pattern. The final expression that equals n² involves taking the last and penultimate terms and adjusting them such that each term in the series becomes n.

This manipulation reveals that adding up n terms of n results in
`2n²`. This reflects the power of summation simplification techniques used in mathematical series and sequences. The binomial theorem is also mentioned as a type of series expansion, though it isn't directly related to the initial series sum problem. In physics and statistics contexts, formulas concerning the Central Limit Theorem and standard deviation are provided highlighting different types of series and summations in those fields.