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![[Post New]](/templates/default/images/icon_minipost_new.gif) 16 Apr 2008 17:09:40 IST
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The largest term of the sequence 1/503 4/524 9/581 16/692........ is a 16/92 b 4/524 c 49/1529 d none of these
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16 Apr 2008 18:17:53 IST
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the terms are:
1^2 / 500 + 3*1^3
2^2 / 500 + 3*2^3
3^2 / 500 + 3*3^3
4^2 / 500 + 3*4^3
=
n^2 / 500 + 3*n^3
differentiate and equate to 0:
(500 + 3*n^3) (2n) - n^2(9n^2) = 0
1000 + 6n^3 = 9n^3
1000 = 3n^3
n = 10 / cube root 3
n = 6.9 approx
so max term is
n^2 / 500 + 3*n^3
= 7^2 / 500 + 3*7^3
= 49 / 1529
so none of the above
:)
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- Gaurav Ragtah (spideyunlimited)
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16 Apr 2008 18:19:38 IST
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