Coursework.Info - Inspiration in an Instant

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#1 Series and Induction In this portfolio, I will be investigating a pattern and forming conjectures to explain what happens when k = 2, 3, or 4 in the 1k + 2k k + 3 k + 4 k + ... + n k series. To do this, I will be using the knowledge that 1 + 2 + 3 + ... + n =. 1. where a1 = 1 x 2 a1 = 1 x 2 a2 = 2 x 3 a3 = 3 x 4 a4 = 4 x 5 . . . Expression seems to show that an = n(n+1) 2. Consider Sn = a1 + a2 + a3 + ... + an where ak is defined in #1 [ak = n(n+1)] a) Determine several values of Sk, including S1, S2, S3, ..., S6 S1 = a1 = 1 x 2 = 2 S2 = a1 + a2 = S1...

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