a) Simplify the following: 6(1 + 4) 6(1+ 4+ 9) 6(1+4+ 9+ 16) 1.2' 2.3 3.4 4.5 b) Based on your "experimental" results from part a), make a general conjecture, in the form of an equation that you think will be true for all positive integers n, whose left-hand side for n = 1,2, 3, 4 gives you the four fractions listed in part a) (and whose right-hand side agrees with the results you found). Do not try to prove your conjecture at this stage. Assuming your conjecture from part b) is true, what expression do you get for 1+4+9+ ··+n² ? Again, don't worry about proving this yet.

a) Simplify the following: 6(1 + 4) 6(1+ 4+ 9) 6(1+4+ 9+ 16) 1.2' 2.3 3.4 4.5 b) Based on your "experimental" results from part a), make a general conjecture, in the form of an equation that you think will be true for all positive integers n, whose left-hand side for n = 1,2, 3, 4 gives you the four fractions listed in part a) (and whose right-hand side agrees with the results you found). Do not try to prove your conjecture at this stage. Assuming your conjecture from part b) is true, what expression do you get for 1+4+9+ ··+n² ? Again, don't worry about proving this yet.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.4: Mathematical Induction

Problem 46E

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