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[SOLVED] Infinite series help
[tex]\sum- (\frac{5}{4})^n[/tex]
i=infinity and n=0
Convergence of a geometric series
[tex]\sum (ar)^n = a/(1-r) when 0<|r|<1[/tex]
I have to explain why this series diverges or converges. The test for divergence gives an answer of infinity so it diverges. The terms are 1, -5/4, 25/16, -125/64, 625/256... To me it looks like a geometric series with r=|-5/4| which diverges because |-5/4|[tex]\geq[/tex] 1. Is this correct?
Homework Statement
[tex]\sum- (\frac{5}{4})^n[/tex]
i=infinity and n=0
Homework Equations
Convergence of a geometric series
[tex]\sum (ar)^n = a/(1-r) when 0<|r|<1[/tex]
The Attempt at a Solution
I have to explain why this series diverges or converges. The test for divergence gives an answer of infinity so it diverges. The terms are 1, -5/4, 25/16, -125/64, 625/256... To me it looks like a geometric series with r=|-5/4| which diverges because |-5/4|[tex]\geq[/tex] 1. Is this correct?