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If p is a prime, then sum of log(p)p^(...

If p is a prime, then sum of
`log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=`

A

`1+log2`

B

`1+log3`

C

`1-log2`

D

`2-log2 `

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(B) (HOME WORK)
  1. The 4^(th) term of "log"(e )(3)/(2) is

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  2. Coefficient of x^(n) in log(e )(1+(x)/(2)) is

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  3. If p is a prime, then sum of log(p)p^(1//2)-log(p)p^(1//3)+log(p)p^(...

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  4. log(2)e-log(4)e+log(8)e-…….oo=

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  5. log5-(log25)/(2^(2))+(log125)/(3^(2))-(log625)/(4^(2))+ ……

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  6. (1)/(2.3)+(1)/(4.5)+(1)/(6.7)+……oo=

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  7. (1)/(1.2)+(1)/(3.4)+(1)/(5.6)+....

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  8. Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^...

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  9. -((4)/(5)+(4^(2))/(5^(2).2)+(4^(3))/(5^(3).3)+(4^(4))/(5^(4).4)+……oo)=

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  10. y=(x^(3)+(x^(6))/(2)+(x^(9))/(3)+……) then

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  11. If |x|lt 1, tnen the coefficient of x^(5) in the expansion of (1-x)log...

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  12. (1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=

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  13. (x)/(x+1)+(1)/(2)((x)/(x+1))^(2)+(1)/(3)((x)/(x+1))^(3)+....=

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  14. The 3^(rd) term in log((1)/(1-x)) is

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  15. n^(th) term of log(e )(6//5) is

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  16. 2log x-log(x+1)-log(x-1)=

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  17. If x^(2)y=2x-y then y^(2)+(y^(4))/(2)+(y^(6))/(3)+…oo=

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  18. If higher powers of x^(2) are neglected, then the value of log(1+x^(2)...

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  19. If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1...

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  20. Assertion (A) : coefficient x^(n) in log(1+x) is ((-1)^(n-1))/(n) when...

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