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If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/...

If `1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^2)+` equals `pi^2//8` b. `pi^2//12` c. `pi^2//3` d. `pi^2//2`

A

`pi^(2)//6`

B

`pi^(2)//16`

C

`pi^(2)//8`

D

none of these

Text Solution

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The correct Answer is:
C
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FIITJEE-PROGRESSION & SERIES -ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. If H1. H2...., Hn are n harmonic means between a and b(!=a), then the ...

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  2. The largest interval for which the series 1+(x-1)+(x-1)^(2)+….oo may ...

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  3. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

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  4. Let Tr a n dSr be the rth term and sum up to rth term of a series, res...

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  5. Let a1,a2,a3... be in A.P. and ap,aq,ar be in G.P. then value of aq/ap...

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  6. If H(1),H(2),H(3),…..H(2n+1) are in H.P then sum(i=1)^(2n)(-1)^(j)((H(...

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  7. If the sequences 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8….. where n consecutive ...

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  8. If S(r)= sum(r=1)^(n)T(1)=n(n+1)(n+2)(n+3) then sum(r=1)^(10) 1/(T(r))...

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  9. a,b,c,d,e are five numbers in which the first three are in A.P and th...

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

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  11. Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+... is

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  12. The sum of n terms of the series 5/(1.2). 1/3 +7/(2.3). 1/(3^(2))+9/(...

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  13. Let tr=2^(r/2)+2^(-r/2) then sum(r=1)^10 tr^2=

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  14. In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose...

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  15. Let a(1),a(2),a(3),a(4),a(5) be a five term geometric sequence satisfi...

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  16. The nth term of the series 10,23,60,169,494 , …….. is

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  17. The value of sum(n=0)^(m) log ((a^(2n-1))/(b^(m-1)))(a != 0 , 1 , b ...

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  18. A , r = 1 , 2, 3 ….., n are n points on the parabola y^(2)=4x in the...

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  19. Sum to n terms of the series 1^(3) - (1.5)^(3) +2^(3)-(2.5)^(3) +…. is

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  20. Find the sum of the product of every pair of the first n of natural n...

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