Series Notation Calculator

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Example

Created on 2024-06-20Asked by Isabella Flores (Solvelet student)

Express the sum

1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots

in series notation and determine its sum.

Solution

To express the sum

1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots

in series notation and determine its sum: 1. **Recognize the series as a geometric series:**

\sum_{n=0}^{\infty} \left(\frac{1}{2}\right)^n.

2. **Use the formula for the sum of an infinite geometric series:** For

|r| < 1

\sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}.

Here,

a = 1

and

r = \frac{1}{2}

. 3. **Calculate the sum:**

\sum_{n=0}^{\infty} \left(\frac{1}{2}\right)^n = \frac{1}{1 - \frac{1}{2}} = 2.

Therefore, the sum of the series is

2

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Ella Brown on Solvelet

1. Write the series

\sum_{n=1}^\infty \frac{2^n}{n}

using sigma notation.2. Express the sum of the series

1 + 2 + 4 + \ldots + 2^n

in sigma notation.,

DefinitionThis is called series notation, or summation notation, which is the use of the Greek letter sigma Σ to represent the sum of a sequence of terms. It is a compact way to write a series sum. Example: First n natural number series can be written as ∑i=1ni=1+2+3+…+n,

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