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If S(1),S(2)andS(3) denote the sum of fi...

If `S_(1),S_(2)andS_(3)` denote the sum of first `n_(1)n_(2)andn_(3)` terms respectively of an A.P., then
`(S_(1))/(n_(1))(n_(2)-n_(3))+(S_(2))/(n_(2))+(n_(3)-n_(1))+(S_(3))/(n_(3))(n_(1)-n_(2))`=

A

0

B

1

C

`S_(1)S_(2)S_(3)`

D

`n_(1)n_(2)n_(3)`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-SEQUENCES AND SERIES-Exercise
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  2. If |x|<1a n d|y|<1, find the sum of infinity of the following series: ...

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  3. If S(1),S(2)andS(3) denote the sum of first n(1)n(2)andn(3) terms resp...

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

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  6. 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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  7. If, for 0ltxltpi//2, y=exp[(sin^(2)x+sin^(4)x+sin^(6)+ . . .. oo)log...

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  8. The value of 0. 2^(logsqrt(5)1/4+1/8+1/(16)+) is 4 b. log4 c. log2 d....

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

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  10. If 1/1^2+1/2^2+1/3^2....oo=pi^2/6 then 1/1^2+1/3^2+1/5^2....=

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  11. the value of [(0.16)^(log0.25 (1/3+1/3^2+1/3^3+....................+oo...

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

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

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  14. If a(1),a(2),a(3), . .. . ,a(n) are in A.P. and a(i)gt0 for each i=1,2...

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  15. If 1/(b-a)+1/(b-c)=1/a+1/c , then a,b,c are in (A) AP (B) GP (C) ...

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

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

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

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  19. The coefficient of x^(49) in the product (x-1)(x-3)(x+99)i s -99^2 b....

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

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