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The sum of the first n terms of the seri...

The sum of the first n terms of the series `1^2+2xx2^2+3^2+2xx 4^2+5^2+2xx6^2…..is (n(n+1)^2)/(2)` when n is even .Then find the sum when n is odd.

A

`(n(n+1))/(2)`

B

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

C

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

D

`{(n(n+1))/(2)}^(2)`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
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  2. If a,b,c are in HP, then (a)/(b+c),(b)/(c+a),(c )/(a+b) are in

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  3. The sum of the first n terms of the series 1^2+2xx2^2+3^2+2xx 4^2+5^2+...

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  4. If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P. ...

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  5. If x=2+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove ...

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  6. a ,b ,c are positive real numbers forming a G.P. ILf a x^2+2b x+c=0a n...

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  7. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

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  8. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

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  9. Find the sum of n terms of the sequence (x+1/x)^2,(x^2+1/(x^2))^2,(x^3...

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  10. The geometric mean between -9 and -16 is 12 b. -12 c. -13 d. none of t...

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  11. The sum of n terms of an A.P. is 3n^(2)+5. The number of term which eq...

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  12. If the pth, qth, and rth terms of an A.P. are in G.P., then the common...

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  13. If log2,log(2^x-1)a n dlog2log(2^x+3) are in A.P., write the value of ...

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  14. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  15. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

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  16. a, b, c are sides of a triangle and a, b, c are in GP If log a- log ...

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  17. about to only mathematics

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  18. If x^(a)=x^(b//2)z^(b//2)=z^(c), then a,b,c are in

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  19. A G.P. consists of an even number of terms. If the sum of all the t...

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  20. The interior angles of a polygon are in A.P. the smallest angle is 120...

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