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[" 18."(1)/((1times3))+(1)/((3times5))+(...

[" 18."(1)/((1times3))+(1)/((3times5))+(1)/((5times7))+...+(1)/((2n-1)(2n+1))],[" 19"(1)/(1)+(1)/(1)+(1)/(1)+quad 1]

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(1)/(1times3)+(1)/(3times5)+(1)/(5times7)+(1)/(7times9)+(1)/(9times11)+(1)/(11times13)

lim_(x->oo) [(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+.....+(1)/(n(n+1))]

[(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+......+(1)/(99times100)] =

[(1)/(5)times(1)/(4)],[ (1)/(5)times(7)/(2)]

(2)/(5)times(-(3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)

(2)/(5)times((-3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)

lim_(n rarr oo){(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....+(1)/((2n+1)(2n+3 ))

Lt_(x to oo)((1)/(3.5)+(1)/(5.7)+.....+(1)/((2n+1)(2n+3)))=

By the principle of mathematical induction prove that the following statements are true for all natural numbers 'n' (a) (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+......+(1)/((2n-1)(2n+1)) =(n)/(2n+1) (b) (1)/(1.4)+(1)/(4.7)+(1)/(7.10)+......+(1)/((3n-2)(3n+1)) =(n)/(3n+1)

((1)/(3)times(2)/(9))/((1)/(3)times(1)/(5)+(1)/(3)times(1)/(3)+(1)/(3)times(2)/(9))