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MATH / Let T be the set of all triples (a,b,c) of positive integers for which there exist triangles with side lengths a, b, c. Compute ∑_((a,b,c)∈T)(2^(a))/(3^(b)5^(c)).

Problem

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problem

Let TT be the set of all triples (a,b,c)(a,b,c) of positive integers for which there exist triangles with side lengths a,a, b,b, c.c. Compute ∑(a,b,c)∈T2a3b5c.\sum_{(a,b,c) \in T} \frac{2^a}{3^b 5^c}.
Plain-text mathematical notation (without MathML)
Let T be the set of all triples (a,b,c) of positive integers for which there exist triangles with side lengths a, b, c.  Compute
∑_((a,b,c)∈T)(2^(a))/(3^(b)5^(c)).
Original LaTeX notation
Let $T$ be the set of all triples $(a,b,c)$ of positive integers for which there exist triangles with side lengths $a,$ $b,$ $c.$  Compute
\[\sum_{(a,b,c) \in T} \frac{2^a}{3^b 5^c}.\]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
7dd972d1-3d73-59a6-9921-9bb6f52c46ff
task_key
intermediate~5falgebra--test--7dd972d1-3d73-59a6-9921-9bb6f52c46ff
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import