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

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)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))}=

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

underset(n to oo)lim (5^(n)+1)/(3^(n)-1)=

underset(n to oo)lim (2^(n)-1)/(3^(n)+1)=

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

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

lim_(n rarr oo)((1)/(1.3)+(1)/(3.5)+.............+(1)/((2n-1)(2n+) 1)))

underset(n to oo)lim (2^(1//n)-1)/(2^(1//n)+1)=