Series Notation

Series notation is nothing but the sum of terms. This sum of term series form is called a series notation. The other name of series notation is called summation notation or sigma notation. When we expand the summation or sigma notation, then it is called series notation. In this article we see about the series notation with example problem.

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Series Notation:

For example: x = 1 + 2 + 3 ---- n, the expand form of summation is 1 + 2 + 3 ---- n said to be as series notation.

Thus we write the series term by replace the given variable in function using limit given in summation. Let us see the example problem in series notation.
Example Problem – Series Notation:

Example 1:

Write the series notation of the expression and find the value (3 + 2x)

Solution:

Given: (3 + 2x)

Step 1: Expand the given summation notation to find the series notation.

(3 + 2x) = (3 + 21) + (3 + 22) + (3 + 23) + (3 + 24)

Thus the series notation is (3 + 21) + (3 + 22) + (3 + 23) + (3 + 24)

Step 2: Find the value of the series notation.

= (3 + 21) + (3 + 22) + (3 + 23) + (3 + 24)

= (3 + 2) + (3 + 4) + (3 + 8) + (3 + 16)

= 5 + 7 + 11 + 19

= 42

Answer: (3 + 2x) = 42

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Example 2:

Which of the following is the series notation of the expression (2 + y)?

Option:

a)     (2 * 1) + (2 * 2) + (2 * 3) + (2 * 4)

b)    (2 + 1) * (2 + 2) * (2 + 3) * (2 + 4)

c)     1 + 2 + 3 + 4

d)    (2 + 1) + (2 + 2) + (2 + 3) + (2 + 4)

Solution:

Given: (2 + y)

(2 + y) = (2 + 1) + (2 + 2) + (2 + 3) + (2 + 4)

Answer: Option d