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The sum of 10 terms of the series (x+1/...

The sum of 10 terms of the series `(x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)^2+....` is

A

`((x^20-1)/(x^2-1))((x^22+1)/x^20)+20`

B

`((x^18-1)/(x^2-1))((x^11+1)/x^9)+20`

C

`((x^18-1)/(x^2-1))((x^11-1)/x^9)+20`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
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  2. The series of natural number is divided into groups as follows , (1), ...

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  3. The sum of 10 terms of the series (x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)...

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  4. If the sequence 1,2,2,4,4,4,4,,8,8,8,8,8,8,8,8,.... where n consecutiv...

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

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  6. The cubes of the natural numbers are grouped as 1^3,(2^3,3^3),(4^3,5^3...

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  7. Let f(n)=[1/2+n/100] where [x] denote the integral part of x. Then th...

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  8. ABC is a right angled triangle in which angleB=90^@ and BC=a. If n poi...

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  9. If a,b,c are three distinct positive real number such that a^2+b^2+c^2...

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  10. The sum of the series 1^3 - 2^3 + 3^3 - ....+ 9^3=

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  11. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

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  12. Let two numbers have arithmetic mean 9 and geometric mean 4. Then thes...

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  13. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

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  14. Let a1 , a2 , a3,.... be terms of an A.P. if (a1 + a2 +....+ ap)/(a1 +...

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  15. If a1,a2,.....an are in H.P., then the expression a1a2 + a2a3 + ... + ...

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  16. If the sum of first n natural numbers is 1/5 times the sum of their sq...

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  17. log3 2 , log6 2 and log12 2 are in

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  18. If x be the AM and y,z be two GM's between two positive numbers, then ...

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  19. If In (a + c), In(c - a) , In(a - 2b + c) are in A.P., then

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