1+(4)/(2!)+(7)/(3!)+(10)/(4!)+....=...

`1+(4)/(2!)+(7)/(3!)+(10)/(4!)+....=`

`e+2`

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underset(n to oo)lim {(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+....+(1)/((3n-2)(3n+1))}=

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Which group of fractions are like fractions among the following? (i) (2)/(7), (3)/(7), (4)/(7) (ii) (1)/(2), (2)/(9), (4)/(9) (iii) (3)/(7), (4)/(9), (7)/(11)

If (3)/(4)+(1)/(3)((3)/(4))^(3)+(1)/(5)((3)/(4))^(5)+....=log_(e)a,(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=log_(e)b, 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=log_(e)c then the ascending order of a, b, c is

Let S = (1)/( 1.4) + (1)/( 4.7) + (1)/(7.10) + .....n terms, Observe the following lists. {:("List-I","List-II"),("A)" underset(n to prop) (Lt) S=, "1)"0 ),("B)" underset(n to 0 ) (Lt) S=,"2)" 3//10),("C)" underset(n to 3) (Lt) S=,"3)"1//3),("D)" underset(n to 4) (Lt) S=,"4)"1),(,"5)"4//13):}

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

1+(3)/(1!)+(5)/(2!)+(7)/(3!)+....=
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(3)/(2!)+(5)/(3!)+(7)/(4!)+(9)/(5!)+....=
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1+(4)/(2!)+(7)/(3!)+(10)/(4!)+....=
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underset(n=1)overset(oo)Sigma(2n)/((2n+1)!)=
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underset(n=1)overset(oo)sum(n^(2))/((n+1)!)=
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underset(n=1)overset(oo)Sigma(2n^(2)+n+1)/(n!)=
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(1+(1)/(2!)+(1)/(4!)+(1)/(6!)+....)^(2)-(1+(1)/(3!)+(1)/(5!)+(1)/(7!)+...
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(1+(a^(2)x^(2))/(2!)+(a^(4)x^(4))/(4!)+....)^(2)-(ax+(a^(3)x^(3))/(3!)...
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(1+(2^(2))/(2!)+(2^(4))/(3!)+(2^(6))/(4!)+....)/(1+(1)/(2!)+(2)/(3!)+(...
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(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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