If the sequence a1, 92, 93, an 2 az-az +az-a +...+ a²n-1-a²n ... ... is an A.P., then prove that n 2n-1 = 2 -(a²-a²n)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 51E
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If the sequence a1, 92, 93, an, ... is an A.P., then prove that
2
a-a+a-ai++an-1-an
...
=
n
- (a²-a²n)
2n-1
Transcribed Image Text:If the sequence a1, 92, 93, an, ... is an A.P., then prove that 2 a-a+a-ai++an-1-an ... = n - (a²-a²n) 2n-1
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