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If S(1),S(2),S(3),"…….",S(2n) are the sa...

If `S_(1),S_(2),S_(3),"…….",S_(2n)` are the same of infinite geometric series whose first terms are respectively `1 , 2, 3,"…….", 2n` and common ratio are respectively.
`1/2, 1/3, '…..". (1)/(2n+1)`.Find the value of `S_(1)^(2) + S_(2)^(2) + "……" + S_(2n-1)^(2)`.

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The correct Answer is:
`( n ( 2n +1) ( 4n +1))/(3) -1 `
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RESONANCE-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
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  2. The sum of three numbers in A.P. is 27, and their product is 504, find...

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  3. The friends whose ages from a G.P. divide a certain sum of money in pr...

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  4. The roots of the equation x^(5)-40x^(4)+ax^

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  5. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

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  6. If a,b,c are in A.P. and if (b-c) x^(2)+(c-a) x+(a-b)=0 and 2 (c+a) x^...

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  7. Along a road lies an odd number of stones placed at intervals of 10m. ...

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  8. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

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  9. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

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  10. If n is any positive integer, then find the number whose square is und...

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  11. Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(2.4.6)...

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  12. If S(1),S(2),S(3),"…….",S(2n) are the same of infinite geometric serie...

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  13. Find the sum to n terms of the series :1^2+(1^2+2^2)+(1^2+2^2+3^2)+dot...

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  14. Let a (l) = (7)/(4) ((2)/(3)) ^( l -1), j in N.lf b (1) = a (j) ^(2)...

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  15. The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple ...

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  16. As show in the figure , the five circles are tangent to one another co...

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  17. The arithmetic mean of the nine number in the given set {9,99,999, ......

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  18. Let a sequence whose n ^(th) term is {a (n)} be defined as a (1) = 1...

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  19. If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2...

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  20. Let K is a positive Integer such that 36 +K , 300 + K , 596 + K are th...

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