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    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)

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    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?
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    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.

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