(a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)...

`(a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/a)^(3)+....`=

`log_(e)(a//b)`

`log_(e)(b//a)`

`log_(e)(a+b)`

`log_(e)(a-b)`

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A = ((1)/(2),(3)/(2)) , B ((3)/(2),(-1)/(2)) then BA = .....

|(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

If the Point (a^3//(a-1),(a^2-3)//(a-1)),(b^2//(b-1),(b^2-3)//(b-1)), and (c^3//c-1,(c^2-3)/(c-1)) , where a,b,c are different from 1, lie on the line lx+my+n=0 then

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Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

If Delta_(1)=|{:(a_(1)^(2)+b_(1)+c_(1),a_(1)a_(2)|b_(2)|c_(2),a_(1)a_(3)+b_(3)+c_(3)),(b_(1)b_(2)+c_(1),b_(2)^(2)+c_(2),b_(2)b_(3)+c_(3)),(c_(1)c_(3),c_(2)c_(3),c_(3)^(2)):}|" and " Delta_(2)=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| , then find the value of (Delta_(1))/(Delta_(2)) .

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

(1)/(2)+(3)/(2).(1)/(4)+(5)/(3).(1)/(8)+(7)/(4).(1)/(16)+....=
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Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^...
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(a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/a)^(3)+....=
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(a-1)-(1)/(2)(a-1)^(2)+(1)/(3)(a-1)^(3)-(1)/(4)(a-1)^(4)+...=
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e^(x-1-(1)/(2)(x-1)^(2)+(1)/(3)(x-1)^(3)-(1)/(4)(x-1)^(4))+...=
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If S=((b-1)-(1)/(2)(b-1)^(2)+(1)/(3)(b-1)^(3)-....)/((a-1)-(1)/(2)(a-1...
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(1)/(x+1)+(1)/(2(x+1)^(2))+(1)/(3(x+1)^(3))+....=
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(x)/(x+1)+(1)/(2)((x)/(x+1))^(2)+(1)/(3)((x)/(x+1))^(3)+....=
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(2ax)/(a^(2)+x^(2))+(1)/(3)((2ax)/(a^(2)+x^(2)))^(3)+(1)/(5)((2ax)/(a^...
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((2n)/(n^(2)+1))+(1)/(3)((2n)/(n^(2)+1))^(3)+(1)/(5)((2n)/(n^(2)+1))^(...
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(1)/(2x-1)+(1)/(3).(1)/((2x-1)^(3))+(1)/(5)(1)/((2x-1)^(5))+....=
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(1)/(2x+1)+(1)/(3)(1)/((2x+1)^(3))+(1)/(5)(1)/((2x+1)^(5))+....=
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(1)/(2n^(2)-1)+(1)/(3(2n^(2)-1)^(3))+(1)/(5(2n^(2)-1)^(5))+....=
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If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)...
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log(1+x+x^(2)+...oo)=
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If |x|lt1 then (1)/(2)x^(2)+(2)/(3)x^(3)+(3)/(4)x^(4)+....=
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(a-1)/(a+1)+(1)/(3)((a-1)/(a+1))^(3)+(1)/(5)((a-1)/(a+1))^(5)+....=
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If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+..., then x =
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If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =
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|a|lt1,b=underset(k=1)overset(oo)Sigma(a^(k))/(k)impliesa=
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