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If a1,a2,a3,... are in A.P. and ai>0 for...

If `a_1,a_2,a_3,...` are in A.P. and `a_i>0` for each i, then `sum_(i=1)^n n/(a_(i+1)^(2/3)+a_(i+1)^(1/3)a_i^(1/3)+a_i^(2/3))` is equal to (a) `(n)/(a_(n)^(2//3)+a_(n)^(1//3)+a_(1)^(2//3))` (b) `(n(n+1))/(a_(n)^(2//3)+a_(n)^(1//3)+a_(1)^(2//3))` (c) `(n(n-1))/(a_(n)^(2//3)+a_(n)^(1//3)*a_(1)^(1//3)+a_(1)^(2//3))` (d) None of these

A

`(n+1)/(a_(n-1)^(2//3)+a_(n-1)^(1//3)a_(1)^(1//3)+a_(1)^(2//3))`

B

`(n-1)/(a_(n)^(2//3)+a_(n)^(1//3)+a_(1)^(2//3))`

C

`(n-1)/(a_(n)^(2//3)+a_(n)^(1//3)+a_(1)^(1//3)+a_(1)^(2//3))`

D

`(n+1)/(a_(n+1)^(2//3)+a_(n+1)^(1//3)+a_(1)^(1//3)+a_(1)^(2//3))`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
  1. If |a| < 1 and |b| < 1, then the sum of the series a(a+b)+a^2(a^2+b^2)...

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  2. If log(x)a, a^(x//2), log(b)X are in G.P. then x is equal to

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  3. If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-...

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  4. If 0ltxlt(pi)/(2) exp [(sin^(2)x+sin^(4)x+sin^(6)x+'.....+oo)log(e)2] ...

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  5. The value of 0.2

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  6. If the sum of an infinitely decreasing G.P. is 3, and the sum of the s...

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  7. If 1/(1^2)+1/(2^2)+1/(3^2)+..." to "oo = pi^2/6, " then " 1/1^2+1/3^2+...

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  8. The value of [(0.16)^(log(2.5)(1/3+1/3^2+1/3^3+….+oo))]^(1/2) is a) 1 ...

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  9. If the sum of the first n terms of series be 5n^(2)+2n, then its secon...

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  10. If x,|x+1|,|x-1| are first three terms of an A.P., then the sum of its...

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  11. If a1,a2,a3,... are in A.P. and ai>0 for each i, then sum(i=1)^n n/(a(...

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  12. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

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  13. If,a,b and c are in H.P then the value of (ac+ab-bc)(ab+bc-ac)/(abc...

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  14. If AM of the number 5^(1+x) and 5^(1-x) is 13 then the set of possible...

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  15. If a,b,c are in A.P then a+1/(bc), b+1/(ca), c+1/(ab) are in

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  16. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

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  17. The coefficient of x^15 in the product (1-x)(1-2x) (1-2^2 x) (1-2^3 ...

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  18. If S(n)=sum(r=1)^(n) a(r)=(1)/(6)n(2n^(2)+9n+13), then sum(r=1)^(n)sqr...

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  19. If sum(r=1)^(n) a(r)=(1)/(6)n(n+1)(n+2) for all nge1, then lim(ntooo) ...

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  20. Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+.....

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