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underset n rarr oo Lt((1)/(3.7)+(1)/(7.1...

underset n rarr oo Lt((1)/(3.7)+(1)/(7.11)+(1)/(11.15)+....(n" terms "))=

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lim_(n to infty) ((1)/(3.7)+(1)/(7.11) +(1)/(11.15)+. . . +(n" terms ")) =

sum of the series (1)/(3*7)+(1)/(7*11)+(1)/(11*15)+

Lt_(n rarr oo)(1+(1)/(n))^(n)

Lt_(n rarr oo)(1+(1)/(n))^(n)

Lt_(n rarr oo)[(1)/(3n+1) + (1)/(3n+2)+…+(1)/(4n)]

The sum of the series (1)/(3xx7)+(1)/(7xx11)+(1)/(11xx15)+.... is

Lt_(n rarr oo)[(1)/(n+1) + (1)/(n+2)+..(1)/(2n)]

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

underset(n to oo)lim {(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/((2n-1)(2n+1))}=