Find a Formula for the Nth Partial Sum of the Series

question 70

Multiple Choice

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
- $$\frac { 2 } { 3 \cdot 1 } + \frac { 2 } { 5 \cdot 3 } + \frac { 2 } { 7 \cdot 5 } + \ldots + \frac { 2 } { ( 2 n + 1 ) ( 2 n - 1 ) } + \ldots$$

• A) \(\frac { 2 n } { 2 ( n + 1 ) } ; 1\)
• B) \(\frac { 2 n } { n + 2 } ; 2\)
• C) \(\frac { 4 n } { 2 n + 1 } ; 2\)
• D) \(\frac { 2 n } { 2 n + 1 } ; 1\)

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Definitions:

Binomial Variable

A variable that has only two possible outcomes or states, usually associated with 'success' or 'failure' in binary outcome experiments.

Religion

A social-cultural system of designated behaviors, practices, morals, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that relates humanity to supernatural, transcendental, or spiritual elements.

Calculate

The process of determining a result numerically using mathematical operations or algorithms.

Mathematical Calculations

Mathematical calculations involve performing operations such as addition, subtraction, multiplication, and division to solve problems or analyze data.