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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1A
- 1+(2)/(1!)+(4)/(2!)+(8)/(3!)+....=
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- 1+(4)/(1!)+(16)/(2!)+(64)/(3!)+....=
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- underset(k=1)overset(oo)Sigma (1)/(k!)(underset(n=1)overset(k)Sigma2^(...
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- 1-(2)/(1!)+(4)/(2!)-(8)/(3!)+....=
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- 1-(3)/(1!)+(9)/(2!)-(27)/(3!)+....=
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- log(e)2+((log(e)2)^2)/(2!)+((log(e)2)^(3))/(3!)+....=
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- log(e)3+((log(e)3)^(2))/(2!)+((log(e)3)^(3))/(3!)+....=
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- 1+2(log(e)a)+(2^(2))/(2!)(log(e)a)^(2)+(2^(3))/(3!)(log(e)a)^(3)+....=
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- 1+x(log(e)2)+(x^(2))/(2!)(log(e)2)^(2)+(x^(3))/(3!)(log(e)2)^(3)+....=
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- xlog(e)a+(x^(3))/(3!)(log(e)a)^(3)+(x^(5))/(5!)(log(e)a)^(5)+...=
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- xlog(e)a+(x^(3))/(3!)(log(e)a)^(3)+(x^(5))/(5!)(log(e)a)^(5)+...=
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- (1-(3)/(1!)+(9)/(2!)-(27)/(3!)+...)(1+(3)/(1!)+(9)/(2!)+(27)/(3!)+.......
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- (1-(2)/(1!)+(4)/(2!)-(8)/(3!)+....)(1+(4)/(1!)+(16)/(2!)+(64)/(3!)+......
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- e^(3x)=
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- e^(-2x)=
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- e^(5x)+e^(-5x)=
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- e^(7x)-e^(-7x)=
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- (e^(5x)+e^(x))/(e^(3x))=
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- (e^(7x)-e^(x))/(e^(4x))=
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- The (n+1) the term in the expansion of e^(5) is
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