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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
- The 7th term of log(e)(5//4) is
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- The nth term of log(e)2 is
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- The nth term of log(2)(3//2) is
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- The nth term of log(e)(4//3) is
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- (3)/(4)+(1)/(3)((3)/(4))^(3)+(1)/(5)((3)/(4))^(5)+....=
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- 2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...]=
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- 2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=
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- 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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