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Omni-MATH / Find the value of ∑_(1≤a<b<c)(1)/(2^(a)3^(b)5^(c)) (i.e. the sum of (1)/(2^(a)3^(b)5^(c)) over all triples of positive integers (a,b,c) satisfying a<b<c).

Problem

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problem

Find the value of ∑1≤a<b<c12a3b5c\sum_{1 \leq a<b<c} \frac{1}{2^{a} 3^{b} 5^{c}} (i.e. the sum of 12a3b5c\frac{1}{2^{a} 3^{b} 5^{c}} over all triples of positive integers (a,b,c)(a, b, c) satisfying a<b<ca<b<c).
Plain-text mathematical notation (without MathML)
Find the value of ∑_(1≤a<b<c)(1)/(2^(a)3^(b)5^(c)) (i.e. the sum of (1)/(2^(a)3^(b)5^(c)) over all triples of positive integers (a,b,c) satisfying a<b<c).
Original LaTeX notation
Find the value of $$\sum_{1 \leq a<b<c} \frac{1}{2^{a} 3^{b} 5^{c}}$$ (i.e. the sum of $\frac{1}{2^{a} 3^{b} 5^{c}}$ over all triples of positive integers $(a, b, c)$ satisfying $a<b<c$).

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Source and history

task_id
746ed217-bd7d-57f0-8c48-297b68017521
task_key
test--746ed217-bd7d-57f0-8c48-297b68017521
task_revision_id
1
config / split
/ test

Official source

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