Determine If the Series Converges or Diverges $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 } { \sqrt { n + 1 } } - \frac { 1 } { \sqrt { n + 3 } } \right)$$

question 429

Multiple Choice

Determine if the series converges or diverges. If the series converges, find its sum.
- $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 1 } { \sqrt { n + 1 } } - \frac { 1 } { \sqrt { n + 3 } } \right)$$

• A) converges; \(\frac { 1 } { \sqrt { 3 } } + \frac { 1 } { \sqrt { 6 } }\)
• B) converges; \(\frac { 1 } { \sqrt { 3 } } + \frac { 1 } { 2 }\)
• C) converges; \(\frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 3 } }\)
• D) diverges

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Definitions:

Complete Counterbalancing

A method in experimental design where all possible orders of presenting stimuli are used across participants to control for order effects.

Repeated Measures

A research design where the same participants are observed multiple times under different conditions.

Posttest-pretest

An analysis framework where the performance or outcomes are examined after the intervention first, followed by comparison to the initial pre-intervention state.

Repeated Measures

A study design in which the same subjects are tested under each condition more than once, allowing for the control of individual differences.