How to show this formal identity (or you can assume

Layla Velazquez

Layla Velazquez

Answered question

2022-06-22

How to show this formal identity (or you can assume | x | < 1

Answer & Explanation

Punktatsp

Punktatsp

Beginner2022-06-23Added 22 answers

Notice that
( 1 + x n + x 2 n ) ( 1 x n + x 2 n ) = 1 + x 2 n + x 4 n
Now if p n is product of first n brackets on LHS then
p n = 1 + x 2 n + x 2 n + 1 1 + x + x 2
Taking lim n p n for | x | < 1 we get the desired.

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