To evaluate the related series of a sequence, you need to find the sum of the terms in the sequence. The provided reference discusses evaluating a series where the index i ranges from a starting value to an ending value.
Here's a breakdown of the process:
- Identify the sequence: Determine the formula or pattern that defines the terms of the sequence.
- Determine the limits: Find the starting and ending values for the index (e.g.,
i = 1to3as in the reference). - Calculate the terms: Substitute each value of the index within the specified limits into the sequence's formula to find the corresponding term.
- Sum the terms: Add all the calculated terms together. This sum is the value of the series.
Example:
Let's evaluate the series Σ i from i = 1 to 3 (as shown in the YouTube reference). This can be written as:
Σ i = 1 + 2 + 3 = 6
- Sequence: i
- Limits: i = 1 to 3
- Terms: 1, 2, 3
- Sum: 1 + 2 + 3 = 6
In essence, evaluating a series involves plugging in the index values within the specified range into the sequence's formula, calculating the resulting terms, and then summing those terms together.
