Lesson 3 of 10 · 8 min
Series and sigma notation
NCERT §8.3
Meera doesn't only care what goes into each jar in a given week. She wants to know what the jar holds in total. That total is a sum of terms, and it has its own name.
The lesson in notes
In short
The series of a sequence a₁, a₂, a₃, … is the expression a₁ + a₂ + a₃ + …. It is finite or infinite according as the sequence is finite or infinite.
A series is the indicated sum; the 'sum of the series' is the number the addition gives. 1 + 3 + 5 + 7 + 9 is a series with 5 terms, and its sum is 25.
Sigma notation writes a series compactly: Σ aₖ with k running from 1 to n means a₁ + a₂ + … + aₙ.
Example: Σ (3k − 1) for k = 1 to 4 is 2 + 5 + 8 + 11 = 26, and Σ k² for k = 1 to 5 is 1 + 4 + 9 + 16 + 25 = 55.
The letter k is only a counter; any other letter gives the same sum. The limits below and above Σ tell where the counting starts and stops.