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The sum of the series 1+(1+a)/(2!)+(1...

The sum of the series
`1+(1+a)/(2!)+(1+a+a^(2))/(3!)+(1+a+a^(2)+a^(3))/(4!)`+…..is

A

`(e^(a)-e)/(a-1)`

B

`(e^(a)-e)/(a+1)`

C

`(e^(2a)+1)/(a-1)`

D

`(e^(a)+e)/(a-1)`

Text Solution

Verified by Experts

The correct Answer is:
a
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OBJECTIVE RD SHARMA-EXPONENTIAL AND LOGARITHMIC SERIES-Exercise
  1. The value of sqrt(c ) rounded off of three decimal places is

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  2. The sum of the series 1+(1+a)/(2!)+(1+a+a^(2))/(3!)+(1+a+a^(2)+a^(3...

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  3. The sum of the series sum(n=1)^(oo)(2n)/((2n+1)!) is

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  4. The value of log(e) e- log(9) e + log(27) e- log(81) e+…infty is

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  5. The sum of the series (4)/(1!)+(11)/(2!)+(22)/(3!)+(37)/(4!)+(56)/(5!)...

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  6. The expansion of (1+(x^(2))/(2!)+(x^(4))/(4!)..)^(2) in ascending powe...

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  7. The coefficent of x^(n) in the expansion of (1+(x^(2))/(2!)+(x^(4))/(4...

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  8. If alpha,beta are the roots of the equation ax^(2)+bx+c=0 then log(a-b...

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  9. The sum of the series 1+(1+2)/(2!)+(1+2+2^(2))/(3!)+(1+2+2^(2)+2^(3)...

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  10. The sum of the series 1+(1^2+2^2)/(2!)+(1^(2)+2^(2)+3^(2))/(3!)+(1^(...

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  11. The coefficent of x^(n) in the series 1+(a+bx)/(1!)+(a+bx)^(2)/(2!)+...

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  12. The sum of the series (1^(2).2^(2))/(1!)+(2^(2).3^(2))/(2!)+(3^(2).4^(...

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  13. The value of (x+y)(x-y)+1/(2!)(x+y)(x-y)(x^2+y^2)+1/(3!)(x+y)(x-y)(x^4...

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  14. If e^(x)=y+sqrt(1+y^(2) then the value of y is

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  15. If (e^(5x)+e^(x))/(e^(3x)) is expand in a series of ascending powers o...

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  16. In the expansion of (e^(7x)+e^(3x))/(e^(5x)) the constant term is

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  17. The value of sqrt(2-1)/sqrt(2)+3-2sqrt(2)/(4)+5sqrt(2-7)/6sqrt(2)+17-1...

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  18. If y=2x^(2)-1 then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…infty equals...

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  19. If S=Sigma(n=2)^(oo) ""^(n)C(2) (3^(n-2))/(n!) then S equals

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  20. If (e^(x))/(1-x) = B(0) +B(1)x+B(2)x^(2)+...+B(n)x^(n)+... , then the ...

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