Problem #PRU-61403

Problems Calculus Derivative Increasing and decreasing. Researching functions Algebra Surds. Rational powers Irrational equations.

15–16 3.0

Problem

Prove the inequality: $\frac{(b_{1} + \dots b_{n})^{b_{1} + \dots b_{n}}}{(a_{1} + \dots a_{n})^{b_{1} + \dots + b_{n}}} \leq {(\frac{b_{1}}{a_{1}})}^{b_{1}} \dots {(\frac{b_{n}}{a_{n}})}^{b_{n}}$ where all variables are considered positive.

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