find-number-of-rational-terms-in-the-expansion-of-3-1-5-2-1-3-15-prove-sum-of-all-irrarional-terms-is-greater-than-sum-of-all-rational-terms-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 148997 by gsk2684 last updated on 02/Aug/21

find number of rational terms in the expansion of ((3)^(1/5) +(2)^(1/3) )^(15) . prove sum of all irrarional terms is greater than sum of all rational terms.

$${find}\:{number}\:{of}\:{rational}\:{terms}\: \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left(\sqrt[{\mathrm{5}}]{\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{2}}\right)^{\mathrm{15}} . \\ $$$${prove}\:{sum}\:{of}\:{all}\:{irrarional}\:{terms}\: \\ $$$${is}\:{greater}\:{than}\:{sum}\:{of}\:{all}\:{rational} \\ $$$${terms}. \\ $$

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