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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1A
- (1+(1)/(3!)+(1)/(5!)+....)/(1+(1)/(2!)+(1)/(4!)+....)=
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- ((1)/(2!)+(1)/(4!)+(1)/(6!)+....)/(1+(1)/(3!)+(1)/(5!)+....)=
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- (1)/(2)-(1)/(3(1!))+(1)/(4(2!))-(1)/(5(3!))+....=
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- (1)/(1!)+(1+2)/(2!)+(1+2+2^(2))/(3!)+....=
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- (1)/(1!)+(1+3)/(2!)+(1+3+3^(2))/(3!)+....=
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- (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+....
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- (2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+....=
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- (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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