Question

Find the partial sum. $$\sum_{n=51}^{100} n-\sum_{n=1}^{50} n$$

   Find the partial sum.
$$\sum_{n=51}^{100} n-\sum_{n=1}^{50} n$$

College Algebra

College Algebra

Ron Larson 9th Edition

Chapter 8, Problem 62

Instant Answer

Solved by Expert Sanchit Jain

06/26/2023

Step 1

Step 1: First, we expand the given expression: $$\sum_{n=51}^{100} n-\sum_{n=1}^{50} n = 51 + 52 + \ldots + 100 - (1 + 2 + \ldots + 50)$$ Show more…

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Find the partial sum. $$\sum_{n=51}^{100} n-\sum_{n=1}^{50} n$$

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Key Concepts

Arithmetic Series

An arithmetic series is a sequence of numbers where the difference between consecutive terms is constant. This concept is crucial for summing sequences because it allows the use of a straightforward formula involving the number of terms, the first term, and the last term to compute the total sum efficiently.

Summation Notation

Summation notation, indicated by the sigma symbol (?), provides a compact way to represent the addition of terms in a sequence. It clearly specifies the starting and ending indices of the summation, enabling the concise expression of partial sums and the manipulation of series in mathematical problems.

Partial Sums

A partial sum is the sum of a specified subset of terms in a sequence. In problems involving arithmetic series, calculating partial sums frequently involves applying the arithmetic series formula to different segments of the series and potentially combining or comparing these sums, as seen when subtracting one partial sum from another.

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