Home
Class 12
MATHS
Let S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1...

Let `S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1)/(sqrt99) + (1)/(sqrt100).` Find [S]
You may use the fact that `(sqrtn lt (1)/(2) ) ( sqrtn + sqrt ( n +1)) lt sqrt ( n +1)` for all integers `n ge 1.`

Text Solution

Verified by Experts

The correct Answer is:
18
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -1 PART -II RMO|3 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SSP|55 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

Similar Questions

Explore conceptually related problems

For all n in N,1+(1)/(sqrt(2))+(1)/(sqrt(3))+(1)/(sqrt(4))++(1)/(sqrt(n))

Find underset( n rarr oo) ("lim") (sqrt( n^(2) + 1)+ sqrt( n ) )/( sqrt( n ^(2) + 1)- sqrt( n ) )

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

Evaluate : 1/( 1 + sqrt (2) ) + 1/( sqrt(2) + sqrt (3) ) + 1/ ( sqrt(3) + sqrt (4) )

lim _( x to oo) (1)/(sqrtn sqrt(n+1))+ (1)/(sqrtn sqrt(n+2)) is equal to :

Prove that 1+(1)/(sqrt2)+(1)/(sqrt3)+....+(1)/(sqrtn) ge sqrtn, AA n in N

If n = 7 + 4sqrt(3) then value of (sqrt(n) + 1/(sqrtn)) is

Find the sum (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ upto 99 terms.

Value of 1/(sqrt2+1)+1/(sqrt3+sqrt2)+1/(sqrt4+sqrt3)+....+1/(sqrt100+sqrt99) is

(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+...(1)/(sqrt(99)+sqrt(100))

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...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |