(d) Consider the sequences (In), (n) defined recursively as follows: In+1 = In 2yn Yn+1 = Yn + 2x for n ≥1, ₁ = 1, 12. i. Calculate 12, y2 and 13, Y3- ii. Show - using induction or otherwise - that for any natural number n, In+Yni = (1+2i)". iii. Hence or otherwise, show that for any natural n, Zn = (V5)” cos(narctan2), n = (V5)” sin(n arctan2).

(d) Consider the sequences (In), (n) defined recursively as follows: In+1 = In 2yn Yn+1 = Yn + 2x for n ≥1, ₁ = 1, 12. i. Calculate 12, y2 and 13, Y3- ii. Show - using induction or otherwise - that for any natural number n, In+Yni = (1+2i)". iii. Hence or otherwise, show that for any natural n, Zn = (V5)” cos(narctan2), n = (V5)” sin(n arctan2).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.2: Sequences, Series And Summation Notation

Problem 45E

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