underset(n=1)overset(oo)sum.^(n)C(0)+.^(...

`underset(n=1)overset(oo)sum.^(n)C_(0)+.^(n)C_(1)+underset(.^(n)P_(n))(.^(n)C_(2))+....+.^(n)C_(n)=`

A

`e-1`

B

`e+1`

C

`e^(2)-1`

D

`e^(2)+1`

Text Solution

Verified by Experts

The correct Answer is:

C

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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1A

(1)/(1!)+(1+3)/(2!)+(1+3+3^(2))/(3!)+....=
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1^(2)+(2^(2))/(2!)+(3^(2))/(3!)+(4^(2))/(4!)+....=
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(1^(2))/(2!)+(2^(2))/(3!)+(3^(2))/(4!)+....=
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(1^(2))/(1!)+(1^(2)+2^(2))/(2!)+(1^(2)+2^(2)+3^(2))/(3!)+....=
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(1^(2).2)/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+....=
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(1^(2).2^(2))/(1!)+(2^(2).3^(2))/(2!)+(3^(2).4^(2))/(3!)+....=
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underset(n=1)overset(oo)sum.^(n)C(0)+.^(n)C(1)+underset(.^(n)P(n))(.^(...
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1-(x^(2))/(2!)+(x^(4))/(4!)-(x^(6))/(6!)+....=
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(1.2)/(1!)+(2.3)/(2!)+(3.4)/(3!)+....=
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1+(1)/(2!)+(1.3)/(4!)+(1.3.5)/(6!)+...=
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If S=(1)/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...."to "oo, then...
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(4)/(1!)+(11)/(2!)+(22)/(3!)+(37)/(4!)+(56)/(5!)+....=
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(5)/(1!)+(7)/(3!)+(9)/(5!)+....=
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The sum of the series 1+(1)/(4.2!)+(1)/(16.4!)+(1)/(64.6!)+...oo is
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1+(2x)/(1!)+(3x^(2))/(2!)+(4x^(2))/(3!)+....=
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1.2+(2.3)/(1!)x+(3.4)/(2!)x^(2)+....=
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(3.5)/(1!)x+(4.6)/(2!)x^(2)+(5.7)/(3!)x^(3)+....=
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If S=(x+y)(x-y)+(1)/(2!)(x+y)(x-y)(x^(2)+y^(2))+(1)/(3!)(x+y)(x-y)(x^(...
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The approximate value of e^(2) is
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x+(x^(2))/(3!)+(x^(3))/(5!)+....=
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