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|a|lt1,b=underset(k=1)overset(oo)Sigma(a...

`|a|lt1,b=underset(k=1)overset(oo)Sigma(a^(k))/(k)impliesa=`

A

`underset(k=1)overset(oo)Sigma((-1)^(k)b^(k))/(k)`

B

`underset(k=1)overset(oo)Sigma((-1)^(k-1)b^(k))/(k!)`

C

`underset(k=1)overset(oo)Sigma((-1)^(k)b^(k))/((k-1)!)`

D

`underset(k=1)overset(oo)Sigma((-1)^(k-1)b^(k))/((k+1)!)`

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+..., then x =

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  2. If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =

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  3. |a|lt1,b=underset(k=1)overset(oo)Sigma(a^(k))/(k)impliesa=

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  4. If y=(1)/(2x^(2)-1)" then "y+(y^(3))/(3)+(y^(5))/(5)+....=

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  5. (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+....=

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  6. (1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

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  7. 3x-(5x^(2))/(2)+(9x^(3))/(3)-(17x^(4))/(4)+....+(-1)^(n-1)((2^(n)+1))/...

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  8. 5x-(13)/(2)x^(2)+(35)/(3)x^(3)-(97)/(4)x^(4)+....=

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  9. The coefficient of x^(n) in the expansion of log(e)(1+3x+2x^(2)) is

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  10. The coefficient of x^(n) in the expansion of log (1-5x+6x)^(2) is

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  11. If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2...

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  12. If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2...

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  13. The expansion of log.(1+x+x^(2))/(1-x+x^(2)) as ascending powers of x ...

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  14. If |x|lt1, the coefficient of x^(3) in the expansion of log(1+x+x^(2))...

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  15. If x is very small and neglecting x^(3) and higher powers of x then th...

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  16. (x)/(1.2)+(x^(2))/(3.4)+(x^(3))/(5.6)+....=

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  17. underset(n=1)overset(oo)sum(x^(n))/(n+2)=

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  18. underset(n=1)overset(oo)sum(x^(n+1//2))/(n+1)=

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  19. sin^(2)theta+(1)/(2)sin^(4)theta+(1)/(3)sin^(6)theta+....=

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  20. cos^(2)theta+(1)/(2)cos^(4)theta+(1)/(3)cos^(6)theta+....=

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