Prove that
1/1001 + 1/1002 + 1/1003 +...................+ 1/3001
lies b/w 1 & 4/3
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4 Answers
WE CAN USE AM>HM FOR FIRST CASE.
(1001+1002+.................................+3001)/2001>2001/(1/1001+1/1002+.............+1/3001)
HENCE,
2001/2*(1001+3001)/2001>2001(1/1001+1/1002.......)
2001>2001(1/1001+1/1002.............)
SO,
1>1/1001 + 1/1002 .............
second part needs a bit more thinking.
62krishna you have made a small mistake in the inequality...
your logic though is correct
1I ' ll prove the next part .
11001 + 11002 + ..........11250 < 2501000 = 14
11251 + 11252 + ...........11500 < 2501500 = 15
11501 + 11502 + ............12000 < 5001500 = 13
12001 + 12002 + ............13001 < 10012000
Adding up , we get reqd . sum , S < 77036000 < 43
Numerical Computation of Integrals should also give the answer .
ricky i think it should be
1/1251 + 1/1252 + . . .. . .. . . .+ 1/1500 < 250/ 1250 = 1/5
