buktikan bahwa 1/2,3/4,5/6...2007/2008<1/√2009
Matematika
shintasilviyant
Pertanyaan
buktikan bahwa 1/2,3/4,5/6...2007/2008<1/√2009
1 Jawaban
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1. Jawaban kautsarmus
misalkan
a=1/2.3/4.5/6...2007/2008
b=2/3.4/5.6/7...2008/2009
ab=1/2.2/3.3/4.4/5...2007/2008.2008/2009=1/2009
maka
a<b
a.a<a.b
a²<ab
a²<1/2009
a<1/√2009
jadi 1/2.3/4.5/6...2007/2008<1/√2009