Find the values of the following limts :
`underset(nrarroo)"lim"(1+2+3+....."to"(3n+2)"terms")/(n+1)^(2)`

Find the values of the following limts : underset(nrarroo)"lim"(1+2+3+...+n)/(n^(2))

Find the values of the follwing limts : underset(nrarroo)"lim"(1.2+2.3+3.4+.....n(n+1))/(n^(3))

Find the values of the following limts : underset(nrarroo)"lim"(1^(2)+2^(2)+3^(2)+...+n^(2))/(n^(3))

Find the values of the following limts : underset(nrarroo)"lim"((1)/(3)+(1)/(3^(2))+(1)/(3^(3))+....+(1)/(3^(n)))

Find the values of the following limts : underset(nrarroo)"lim"(1+(1)/(2)+(1)/(2^(2))+(1)/(2^(3))+...."to n terms")

Evaluate the following limits: lim_(nrarroo)(1^2+2^2+3^2+...+n^2)/n^3

Find the value of the limit lim_(nrarroo)(1^2+2^2+...+n^2)/n^3

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

Evaluate : underset(nrarroo)"lim"(1+sqrt(n))/(1-sqrt(n))

Prove : underset(nrarroo)"lim"(sqrt(n+1)-sqrt(n))=0