Last Updated Sep 27, 2025

Summations Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Summations quickly and effectively.

Learn about Induction for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of Induction for easy recall in your Mathematics exam

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Summations

Summation notation, denoted by the Greek letter Σ, is a compact and efficient way to represent the sum of a sequence of numbers.

In general ;

$$\sum_{i=m}^{n} a_i$$

Is equivalent to :

$$a_m+a_{m+1}+a_{m+2}+...+a_n$$

• n is the upper limit of summation.
• m is the lower limit of summation.
• i is the index of summation, which changes during the summation process.

Example

infoNote

Find the value of :

$$\sum_{i=1}^{4} i$$

---

$$1+2+3+4=:success[10]$$

Example

infoNote

Find the value of :

$$\sum_{i=1}^{3} i^2$$

---

$$1+2^2+3^2=1+4+9=:success[14]$$

Example

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Find the value of :

$$\sum_{i=1}^{3} (2i+1)$$

---

$$(2 \cdot 1+1)+(2 \cdot 2+1)+(2 \cdot 3+1)=:success[15]$$

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