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Prove that 1+18nπ1n−−−√<2.4.6…(2n−2)(2n)1.3.5…(2n−3)(2n−1)<(1+18n+1128n2)π2n−−−√

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( 4 months ago )

Within the confines of the O-level syllabus, prove that:

 

1+18nπ1n<2.4.6(2n2)(2n)1.3.5(2n3)(2n1)<(1+18n+1128n2)π2n1+18nπ1n<2.4.6…(2n−2)(2n)1.3.5…(2n−3)(2n−1)<(1+18n+1128n2)π2n

 

for all positive integer nn, where π1=3.141π1=3.141 and π2=3.142π2=3.142

Using A-level mathematics, show that the result remains true with 

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