[lim_(1/1.3)+(1)/(3.5)+...+(1)/((2n-1)(2n+1)))=],[1/1/3],[1/4]

which of the following limits equal to (1)/(2):(A)lim_(n rarr oo)((1)/(1.3)+(1)/(3.5)+...+(1)/((2n-1)(2n+1)))

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

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

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

Prove the following by the method of induction for all n in N : 1/1.3 + 1/3.5 + 1/5.7+...+ 1 / ((2n-1)(2n+1)) = n / (2n+1)

lim_(n rarr oo)((1)/(1.4)+(1)/(4.7)++(1)/((3n-2)(3n+1))))

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

By the Principle of Mathematical Induction, prove the following for all n in N : 1/1.3+1/3.5+1/5.7+......+ 1/((2n -1)(2n +1))= n/(2n +1) .

underset(n to oo)lim {(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))}=

lim_ (n rarr oo) [(1) / (1.2) + (1) / (2.3) + (1) / (3.4) + ... + (1) / (n (n + 1))] =