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Use the Summation Properties to Evaluate the Series - i=16(3i2)\sum _ { i = 1 } ^ { 6 } ( 3 i - 2 )

question 177

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Use the summation properties to evaluate the series. The following rules may be needed: i=1ni=n(n+1) 2;i=1ni2=n(n+1) (2n+1) 6;i=1ni3=n2(n+1) 24.\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .
- i=16(3i2) \sum _ { i = 1 } ^ { 6 } ( 3 i - 2 )

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Psychoanalysis

A therapeutic approach and theory of psychology developed by Sigmund Freud, focusing on unconscious motivations and conflicts.

Scientific Research

Scientific research is the systematic investigation and study of materials, sources, and phenomena, utilizing methods based on empirical or measurable evidence to expand knowledge.

Carl Rogers

An influential American psychologist who founded the client-centered or person-centered approach to therapy.

Psychoanalysis

A therapeutic approach and theory developed by Sigmund Freud focusing on unconscious motivations and conflicts influencing behavior.

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