Question: Let a and r be given nonzero numbers. (a) Show that and from this conclude that, for r 1, (c) Use the result of

Let a and r be given nonzero numbers.

(a) Show that(1-r)(a +ar+ar + . + ar") = a - ar"+1

and from this conclude that, for r ≠ 1,

(c) Use the result of part (a) to explain why the geometric series diverges for |r|

(d) Explain why the geometric series diverges for r = 1 and r = -1.

(1-r)(a +ar+ar + . + ar") = a - ar"+1

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