The sum of the series loge(3)+(loge(3))^...

The sum of the series `log_e(3)+(log_e(3))^3/(3!)+(log_e(3))^5/(5!)+....+ ` is

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To find the sum of the series \( \log_e(3) + \frac{(\log_e(3))^3}{3!} + \frac{(\log_e(3))^5}{5!} + \ldots \), we can recognize that this series resembles the Taylor series expansion for the hyperbolic sine function, which is defined as: \[ \sinh(x) = \frac{e^x - e^{-x}}{2} \] The Taylor series expansion for \( \sinh(x) \) is given by: ...

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OBJECTIVE RD SHARMA ENGLISH-EXPONENTIAL AND LOGARITHMIC SERIES-Section I - Solved Mcqs

In the expansion of log(10)(1-x),|x|lt1 the coefficient of x^(n) is
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Sum of series 9/(1!)+19/(2!)+35/(3!)+57/(4!)+... (A) 7e-3 (B) 12e-5...
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The constant term in the expansion of (3^(x)-2^(x))/(x^(2)) is
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Sigma(n=1)^(oo) (x^(2n))/(2n-1) is equal to
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Then sum of the series 1+(1+3)/(2!)x+(1+3+5)/(3!)x^(2)+(1+3+5+7)/(4...
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1/(e^(3x))(e^x+e^(5x))=a0+a1x+a2x^2+........=>2a1+2^3a3+2^5a5+......=
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Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C=1-(x^(2))/(2!)+(x^(4))/(4!) T...
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The sum of series 2/(3!)+4/(5!)+6/(7!)+...........oo is :
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The sum of the series S=Sigma(n=1)^(infty)(1)/(n-1)! is
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The sum of the series loge(3)+(loge(3))^3/(3!)+(loge(3))^5/(5!)+....+ ...
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The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...
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(1+3)loge3+(1+3^2)/(2!)(loge3)^2+(1+3^3)/(3!)(loge 3)^3+....oo= (a)28...
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If agt0 and x in R, then 1+(xlog(e)a)+(x^(2))/(2!)(log(e)a)^(2)+(x^(...
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(2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+….infty is equal to
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1+(2x)/(1!)+(3x^(2))/(2!)+(4x^(3))/(3!)+..infty is equal to
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1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2)))+1/6((1)/(2^(3))+(1)/(3^(3)))...
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The sum of series (1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3...
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The sum of the series (1)/(2!)+(1)/(4!)+(1)/(6!)+..to infty is
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If 0ltylt2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)/(5x...
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The sum of the series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+..to infty is...
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