# Proving an Inequality : Let an, n>= 1 be an increasing sequence of positive real numbers. Prove that 1/a1 + 2/(a1 + a2) + .... + n/(a1 +... + an) < 4(1/a1 + 1/a2 + ... + 1/an)

Not what you're looking for? Search our solutions OR ask your own Custom question.

Let an, n>= 1 be an increasing sequence of positive real numbers. Prove that

1/a1 + 2/(a1 + a2) + .... + n/(a1 +... + an) < 4(1/a1 + 1/a2 + ... + 1/an)

Can anything be said about the constant 4?

---

https://brainmass.com/math/basic-algebra/inequality-increasing-sequence-of-positive-real-numbers-58886

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Let be an increasing sequence of positive real numbers. Prove that

Can anything be said about the constant 4?

Solution:

Given: be an increasing sequence of positive real numbers. ...

#### Solution Summary

An inequality is proven. The increasing sequences of positive real numbers for inequalities are determined.

$2.49