Find the value of
show your work! : )

Recall the identity,

(link to proof in the comments)

so that the required sum has a value of

Recall another identity,

which means

Then the sum's value reduces to 1/2.

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.