Determine Whether the Series $\sum _ { n = 1 } ^ { \infty } \cos \left( \frac { \pi } { 2 n ^ { 2 } - 1 } \right)$

question 74

Short Answer

Determine whether the series $\sum _ { n = 1 } ^ { \infty } \cos \left( \frac { \pi } { 2 n ^ { 2 } - 1 } \right)$ is convergent or divergent. If it is convergent, find the sum.

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Definitions:

Cristae

Folded inner membranes within mitochondria that increase the surface area for ATP production during cellular respiration.

Cytosol

The fluid component inside a cell, separate from organelles or structures enclosed by membranes, where various cellular processes occur.

Cisternae

Flattened membrane disks or sacs making up the Golgi apparatus, involved in modifying, sorting, and packaging proteins.

Chromatin

Complex of DNA and proteins that forms chromosomes within the nucleus of eukaryotic cells.