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If S(1), S(2),S(3), are the sums of fir...

If `S_(1), S_(2),S_(3), ` are the sums of first n natural numbers their squares and their cubes respectively, then `S_(3) (1 + 8 S_(1)) = `

A

`S_(2)^(2)`

B

`9S_(2)`

C

`9S_(2)^(2)`

D

none

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
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  2. If the common difference of an A.P is 1 and 6th term is (4 cos^(2) alp...

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  3. If S(1), S(2),S(3), are the sums of first n natural numbers their squ...

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  4. Sum of n terms of (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …. is

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  5. Sum of the series S = 1 + (1)/(2)(1 + 2) + (1)/(3) ( 1 + 2 + 3 ) + (1)...

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  6. If 1^(2)+2^(2)+3^(2)+…..+2003^(2)=(2003)(4007)(334)and(1)(2003)+(2)(20...

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  7. The value of the expression ( 1 + (1)/(omega)) ( 1 + (1)/(omega^(2)...

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  8. If 2nd term of a G.p. is 24 and 5th terms is 81 then the first term is

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  9. If 6th term of a G.P is -1/32 and 9th term is 1/1256, then 11th term =

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  10. Which term of 0.004 + 0.02 + 0.1 + ….. Is 12.5 ?

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  11. Which term of the series 1,2,4,8,……… is 256?

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  12. Sum of 20 terms of 3 + 6 + 12 + …. Is

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  13. If nth term of series is 2^(n) + n, then sum of n terms =

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  14. If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 term...

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  15. How many terms of the series 1 + 3 + 9 + …. Sum to 364 ?

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  16. If (1 - y) (1 + 2x + 4x^(2) + 8x^(3) + 16x^(4) + 32x^(5)) = 1 -y^(6), ...

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  17. In a geometric progression consisting of positive terms each term equa...

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  18. 1 + (0.04) + (0.04)^(2) + …. infty =

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  19. If |x| lt 1, y = x - x^(2) + x^(3) - x^(4) + ….. , the value of x in t...

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  20. If x = 1 + a + a^(2) + …. infty " , " y = 1 + b + b^(2) + …...

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