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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
- 2[((2)/(3))+(1)/(3)((2)/(3))^(3)+(1)/(5)((2)/(3))^(5)+...]=
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- (1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=
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- (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+....=
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- 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=
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- log(4)2-log(8)2+log(16)2-....=
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- log(e)2=
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- (1)/(1.2)+(1)/(3.4)+(1)/(5.6)+....
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- (1)/(2.3)+(1)/(4.5)+(1)/(6.7)+(1)/(8.9)+...
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- (1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=
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- (1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=
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- (1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....
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- (5)/(1.2.3)+(7)/(3.4.5)+(9)/(5.6.7)+....=
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- The sum of the series (1)/(1.3.5)+(1)/(3.5.7)+(1)/(5.7.9)+... is
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- Sum of the series (1)/(4.5.6)+(1)/(5.6.7)+(1)/(6.7.8)+... upto oo is
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- (1)/(1.3)+(1)/(2)((1)/(3.5))+(1)/(3)((1)/(5.7))+....=
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- (2)/(3)+(1)/(2)((2)/(3))^(2)+(1)/(3)((2)/(3))^(3)+....=
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- (1)/(5)+(1)/(2.5^(2))+(1)/(3.5^(3))+(1)/(4.5^(4))+.......=
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- The sum of the series (1)/(2)((1)/(5))^(2)+(2)/(3)((1)/(5))^(3)+(3)/(4...
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- (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+.....
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- (1)/(2)+(3)/(2).(1)/(4)+(5)/(3).(1)/(8)+(7)/(4).(1)/(16)+....=
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