Write the Word or Phrase That Best Completes Each Statement

question 163

Essay

Write the word or phrase that best completes each statement or answers the question.
Use mathematical induction to prove the following statement for all positive integers n.
- $$1 + \frac { 5 } { 7 } + \frac { 25 } { 49 } + \ldots + \left( \frac { 5 } { 7 } \right) ^ { n - 1 } = \frac { 7 } { 2 } \left[ 1 - \left( \frac { 5 } { 7 } \right) ^ { n } \right]$$

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Definitions:

Anxiety

A feeling of worry, nervousness, or unease typically about an imminent event or something with an uncertain outcome.

Cognitive Therapy

A type of psychotherapy that treats mental health conditions by addressing negative patterns of thought.

Decatastrophize

A cognitive-behavioral technique aimed at reducing anxiety by altering catastrophic thinking into more balanced and realistic assessments of situations.

Cognitive Therapy

A form of psychotherapy that emphasizes the importance of thought patterns in the development and maintenance of psychological disorders; it aims to change negative thought patterns to improve emotional state and behavior.