How Many Terms of the Series $\sum _ { m = 2 } ^ { \infty } \frac { 12 } { 6 m ( \ln m ) ^ { 2 } }$

question 1

Short Answer

How many terms of the series $\sum _ { m = 2 } ^ { \infty } \frac { 12 } { 6 m ( \ln m ) ^ { 2 } }$ would you need to add to find its sum to within $0.02$ ?

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Definitions:

Pseudopodia

Temporary, amoeba-like projections of the cell surface which assist in the movement and feeding of some eukaryotic cells.

cAMP

Cyclic AMP, a crucial secondary messenger in various biological functions.

Dictyostelium Discoideum

A species of soil-living amoeba famous for its ability to form multicellular structures when food is scarce, often studied for insights into cellular communication and differentiation.

Algae

A diverse group of photosynthetic organisms, mostly aquatic, that range from single-celled forms to large seaweeds, not classified as plants.