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If the sum of n terms of the series : ...

If the sum of n terms of the series `:`
`(1)/( 1^(3)) +( 1+2)/( 1^(3) + 2^(3)) +(1+2+3)/(1^(3) + 2^(3) + 3^(3)) + "......."` in `S_(n)` , then `S_(n) ` exceeds 199 for all n greater than `:`

A

99

B

50

C

199

D

100

Text Solution

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The correct Answer is:
C
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Let S_(n) = ( 1)/( 1^(3)) + ( 1+2)/( 1^(3) + 2^(3)) +"...." + ( 1+ 2 + "...." + n)/(1^(3) +2^(3)"...."+n^(3)), n = 1,2,3,"....." , Then S_(n) is not greater than :

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