**ERIC Number:**EJ915336

**Record Type:**Journal

**Publication Date:**2011-Mar

**Pages:**5

**Abstractor:**As Provided

**Reference Count:**2

**ISBN:**N/A

**ISSN:**ISSN-0020-739X

Integral Representation of the Pictorial Proof of Sum of [superscript n][subscript k=1]k[superscript 2] = 1/6n(n+1)(2n+1)

Kobayashi, Yukio

International Journal of Mathematical Education in Science and Technology, v42 n2 p235-239 Mar 2011

The pictorial proof of the sum of [superscript n][subscript k=1] k[superscript 2] = 1/6n(n+1)(2n+1) is represented in the form of an integral. The integral representations are also applicable to the sum of [superscript n][subscript k-1] k[superscript m] (m greater than or equal to 3). These representations reveal that the sum of [superscript n][subscript k=1] k[superscript m] can be solved into a factor n(n+1) (proportional to the sum of [superscript n][subscript k=1] k, where m is a positive integer. (Contains 4 figures.)

Descriptors: Pictorial Stimuli, Mathematics Instruction, Validity, Mathematical Logic, Equations (Mathematics), Visual Aids, Algebra

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A