m Identities k=1 m 1 [m(m + 1)] and k k=1 = 1 [m(m +...

 

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m Identities Σκ k=1 m 1 [m(m + 1)] and Σk² k=1 = 1 [m(m + 1)(2m +1)] are given. First write the sum 1² +4² +7² +10² +...+(6n+1)² in sigma notation and then use the identities to prove that 1² +4² +7² +10² + ... + (6n + 1)² = (2n + 1)(12n² + 9n + 1). m Identities Σκ k=1 m 1 [m(m + 1)] and Σk² k=1 = 1 [m(m + 1)(2m +1)] are given. First write the sum 1² +4² +7² +10² +...+(6n+1)² in sigma notation and then use the identities to prove that 1² +4² +7² +10² + ... + (6n + 1)² = (2n + 1)(12n² + 9n + 1).