Question

find the generating function for the sequence {1,-1,1,-1}​

Answer 1

Answer:

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Answer 2

Given: ${1,-1,1,-1,....}$

To find: the generating function.

Solution:

Know that the infinite geometric series is$\[1 + z + {z^2} + {z^2} + ----- = \frac{1}{{1 - z}}\]$

Find the generating function of the given sequence.

$\[\left\{ {1, - 1,1, - 1} \right\} \leftrightarrow 1 - x + {x^2} - {x^3} + {x^4} - ----- = \frac{1}{{1 + x}}\]$

Hence, the generating function for the sequence is $\[\frac{1}{{1 + x}}\]$.