# Concavity, derivations, and proofs

Please see attachment

Determine whether....converge or diverge

...derive a necessary condition for the equation...to have a rational root. Then use this condition to prove...

Using binomial coefficients, derive a formula for the nth derivative of the product of two functions.

Suppose that f(x) has a continuous first derivative for all x in R. Prove that f(x) is concave if and only if....

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#### Solution Summary

This contains four parts: determining whether given series converge or diverge, deriving a condition for an equation to have a rational root and using that condition in a proof, deriving a formula for the nth derivative of the product of two functions, and a set of three proofs regarding concavity.

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