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In the expansion of log(10)(1-x),|x|lt1 ...

In the expansion of `log_(10)(1-x),|x|lt1` the coefficient of `x^(n)` is

A

`-(1)/(n)`

B

`-(1)/(n)log10^(e )`

C

`(1)/(n)`

D

`(1)/(n)log10^(e )`

Text Solution

Verified by Experts

`log_(10)(1-x)=log_(10)exx(log_(e))(1-x)=-(log_(10)e)underset(r=1)overset(infty)Sigma (x^(r ))/(r )`
coefficient of `x^(n) in log_(10)(1-x)=(-log_(10)e)/(n)`
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OBJECTIVE RD SHARMA-EXPONENTIAL AND LOGARITHMIC SERIES-Section I - Solved Mcqs
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  2. In the expansion of (e^(x)-1-x)/(x^(2)) is ascending powers of x the f...

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  3. In the expansion of log(10)(1-x),|x|lt1 the coefficient of x^(n) is

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  9. Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C=1-(x^(2))/(2!)+(x^(4))/(4!) T...

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  10. The sum of series 2/(3!)+4/(5!)+6/(7!)+...........oo is :

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  11. The sum of the series S=Sigma(n=1)^(infty)(1)/(n-1)! is

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  12. The sum of the series loge(3)+(loge(3))^3/(3!)+(loge(3))^5/(5!)+....+ ...

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  13. The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...

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  14. (1+3)loge3+(1+3^2)/(2!)(loge3)^2+(1+3^3)/(3!)(loge 3)^3+....oo= (a)28...

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  15. If agt0 and x in R, then 1+(xlog(e)a)+(x^(2))/(2!)(log(e)a)^(2)+(x^(...

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  16. (2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+….infty is equal to

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  17. 1+(2x)/(1!)+(3x^(2))/(2!)+(4x^(3))/(3!)+..infty is equal to

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  18. 1/2(1/2+1/3)-1/4(1)/(2^(2))+(1)/(3^(2))+1/6(1)/(2^(3))+(1)/(3^(3))+…in...

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  19. The sum of series (1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3...

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  20. The sum of the series (1)/(2!)+(1)/(4!)+(1)/(6!)+..to infty is

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