RMO PRACTICE CONTINUES.........

Prove that

1/1001 + 1/1002 + 1/1003 +...................+ 1/3001
lies b/w 1 & 4/3

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.

62
Lokesh Verma ·

krishna you have made a small mistake in the inequality...

your logic though is correct

1
Ricky ·

I ' 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

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