Sigma Notation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Evaluate โˆ‘i=043i\displaystyle\sum_{i=0}^{4} 3^i.

Solution

  1. 1
    Terms: 30=1,โ€…โ€Š31=3,โ€…โ€Š32=9,โ€…โ€Š33=27,โ€…โ€Š34=813^0=1,\; 3^1=3,\; 3^2=9,\; 3^3=27,\; 3^4=81.
  2. 2
    Sum: 1+3+9+27+81=1211+3+9+27+81 = 121.

Answer

121121
This is a finite geometric series with a=1a=1, r=3r=3, 5 terms. Formula: 1(35โˆ’1)3โˆ’1=2422=121\frac{1(3^5-1)}{3-1} = \frac{242}{2} = 121.

About Sigma Notation

Sigma notation uses the Greek letter ฮฃ to express the sum of many terms compactly. The expression โˆ‘i=1nai\sum_{i=1}^{n} a_i means 'add up aia_i for every integer ii from 1 to nn.' For example, โˆ‘i=14i2=1+4+9+16=30\sum_{i=1}^{4} i^2 = 1 + 4 + 9 + 16 = 30.

Learn more about Sigma Notation โ†’

More Sigma Notation Examples

Example 1 easy

Expand and evaluate [formula].

Example 2 medium

Write [formula] in sigma notation and evaluate the closed form for [formula].

Example 4 medium

Rewrite [formula] using linearity of summation.

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