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If a(1),a(2),….a(n) are in arthimatic pr...

If `a_(1),a_(2),….a_(n)` are in arthimatic progression, where `a_(i)gt0` for all I, then show that
`1/(sqrt(a_(1))+sqrt(a_(2)))+1/(sqrt(a_(2))+sqrt(a_(3)))+…+1/(sqrt(a_(n-1))+sqrt(a_(n)))`
`(n-1)/(sqrt(a_(1))+sqrt(a_(n)))`

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NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Exercise 9B
  1. (a) The nth term of a progression is (3n + 5). Prove that this progres...

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  2. (a) Find the 10th term of the progression 1 + 3 + 5 +7+ ... (b) Find...

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  3. (a) Which term of the progression 4 + 8 + 12 + ... is 76 ? (b) Which...

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  4. (a) Find the 16th term from the end of the progression 3 + 6 + 9 + ......

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  5. (a) How many numbers of two digits are divisible by 3 ? (b) How man...

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  6. (a) Find the value of 'x if x + 1, 2x + 1 and x + 1 are in A.P. Also f...

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  7. (a) The 3rd and 19th terms of an A.P. are 13 and 77 respectively. Find...

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  8. Given that the (p+1)th term of an A.P. is twice the (q+1)th term, prov...

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  9. The 12th term of an A.P. is 14 more than the 5th term. The sum of thes...

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  10. (a) Is 303, a term of the progression 5, 10, 15, ... ? (b) Is 38, a...

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  11. Prove that the sum of nth term from the beginning and nth term from th...

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  12. In an A.P., prove that : T(m+n) + T(m-n) = 2*T(m)

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  13. (i) 10 times the 10th term and 15 times the 15th term of an A.P. are e...

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  14. Which term of the A.P. (16-6i,)(15-4i), (14-2 i), ... is a : (a) pur...

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  15. (a) Which term of the progression 10,9(1)/(3),8 (2)/(3),...is the firs...

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  16. Each of two arithmetic progressions 2, 4, 6, ... and 3, 6, 9, ... are ...

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  17. If a(1),a(2),….a(n) are in arthimatic progression, where a(i)gt0 for a...

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  18. If the numbers a , b , c , d , e form an A.P. , then find the value of...

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