Vault Of Euclid

Evaluating a Linear Finite Sum

The definite integral warmup

Evaluate \( \sum_{i=1}^{n} (3i - 1) \).
summationsigma-notationarithmetic-progressionfinite-serieslinearity-of-summationsum-of-integersclosed-formalgebrafactoringriemann-sum-preliminarycalculus-i

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

What this problem tests

Tests the ability to manipulate sigma notation, apply standard sum formulas, and perform algebraic simplification.

This type of summation is a fundamental skill often practiced before introducing Riemann sums in Calculus I.

More on The definite integral