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Sum of a Geometric Series
All the green triangles are similar, and the big triangle is similar to the green triangles.
The ratio of the big triangle's sides is equal to the ratio of the sides for those triangles, so that
, and then
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
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Reference: J. H. Webb, "Proof without Words:
,"
Mathematics Magazine
,
60
(3), 1987 p. 177.
RELATED LINKS
Geometric Series
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Sum of a Geometric Series
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/SumOfAGeometricSeries/
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
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Related Topics
Calculus
Series
Theorem Proving
Triangles
High School Calculus and Analytic Geometry
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Related Curriculum Standards
US Common Core State Standards, Mathematics
HSA-SSE.B.4
HSF-BF.A.2
HSF-LE.A.2
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