Question

1/2,3/4,5/6..........2007/2008 < 1/√2009 ( satu per akar 2009 )

Answer 1

Bukti bahwa :
1/2 . 3/4 . 5/6 . .... 2007/2008 < 1/√2009

misal P = 1/2 . 3/4 . 5/6 .... . 2007/2008 < 1/√2009
Q = 2/3 . 4/5 . 6/7 . .... . 2008/2009

PQ = 1/2. 2/3. 3/4. 4/5 . ... . 2007/2008 . 2008/2009 = 1/2009
jelas bahwa,
P < Q
kedua ruas dikali P, diperoleh :
P² < PQ
P² < 1/2009
P < √(1/2009)
P < 1/√2009

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