Prove That $$\sum _ { j = n } ^ { 2 n - 1 } ( 2 j + 1 ) = 3 n ^ { 2 } \text { for all positive integers } n$$

question 36

Essay

Prove that $$\sum _ { j = n } ^ { 2 n - 1 } ( 2 j + 1 ) = 3 n ^ { 2 } \text { for all positive integers } n$$

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Definitions:

Clitoral Orgasm

An orgasm achieved by the stimulation of the clitoris, a sensitive erogenous zone on the female body.

Sigmund Freud

An Austrian neurologist who is known for founding psychoanalysis, a method for treating psychopathology through dialogue between a patient and a psychoanalyst.

Kinsey

Refers to Alfred Kinsey, an American biologist known for his research into human sexuality in the mid-20th century.

Masters and Johnson

Pioneering sex researchers who studied human sexual response and sexual disorders in the mid-20th century.