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How Many Coefficients in the Binomial Series Expansion Of (1+x)7( 1 + x ) ^ { 7 }

question 101

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How many coefficients in the binomial series expansion of (1+x) 7( 1 + x ) ^ { 7 } are divisible by 7?


Definitions:

Adaptive Radiation

The evolutionary process where organisms rapidly diversify into a multitude of new forms, particularly when a change in the environment makes new resources available.

Beetle Lineage

The evolutionary history and classification of beetles, a diverse group of insects with a hard exoskeleton and over 350,000 species.

Hard Shells

Rigid external coverings that provide protection to the bodies of certain animals, like mollusks and turtles.

Reptiles

A class of cold-blooded, air-breathing vertebrates characterized by their skin covered in scales or hard plates, laying eggs, and typically having a three-chambered heart.

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