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Let S (n ) = sum ( k =0) ^(n) (1)/( sqr...

Let ` S _(n ) = sum _( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k)` What is the value of `sum _( n -1) ^( 90) (1)/( S _(n ) + S _( n -1)) ?=`

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RESONANCE-SEQUENCE & SERIES -EXERCISE -2 (PART -I PREVIOUS ASKED QUESTION FOR PRE RMO)
  1. Let S (n ) = sum ( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k) What is th...

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  2. Let m be the smallest odd positive iteger for which 1 + 2+ …..+ m is a...

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  3. What is the the maximum possibe value of k for which 2013 can be writt...

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  4. The first term of a sequence is 2014. Each succeeding term is the sum ...

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  5. A sequence of positive (a (1), a (2)…a (n)) is called good if a (1) =a...

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  6. A new sequence is obtained from the sequence of positive integers 1,2,...

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  7. Let E(n) denote the sum of the even digits of n. For example, E (1243)...

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  8. Consider the sequence 1,3,3,5,5,5,5,5,7,7,7,7,7,7,7,…… and evaluate it...

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  9. Find the value of the expression ((3 ^(4) + 3 ^(2) +1) .(5 ^(4) + 5 ...

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  10. Let S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1)/(sqrt99) + (1)/(sqrt100). Fi...

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  11. For positive real numbers x and y, define their special mean to be ave...

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  12. Let u,v,w be real numbers in geometric progression such that u gt v gt...

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  13. Let the sum sum ( n =1) ^(g) (1)/(n ( n +1) ( n +2)) written in its lo...

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  14. Suppose x is a positive real number such that {x}, [x] and x are in th...

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  15. Five distinct 2-digit numbes are in a geometric progression. Find the ...

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  16. Let N = 6 + 66+ 666+…+ 666…66, where there are hundred 6's in the last...

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  17. What is the value of sum (1+j = odd 1 le | lt | le 10) (i +j) - sum(1 ...

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  18. A book is published in three volumes, the pages being numbered from 1 ...

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