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+3+...+n)/(n^(2))

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+2+3+....."to"(3n+2)"terms")/(n+1)^(2)

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 : underset(nrarroo)"lim"(2n^(2)+3n-9)/(3n^(3)+2n+7)

Evaluate : underset(nrarroo)"lim"(3n^(2)-4n+6)/(n^(2)+6n-7)

Evaluate : underset(nrarroo)"lim"(n^(4)-n^(2)+6n+1)/(2n^(4)-5n+4)

Prove that underset(nrarroo)"lim"(1^(3)+2^(3)+3^(3)+...+n^(3))/(n^(4))=(1)/(4)

underset(nrarroo)"lim"(-3n+(-1)^(n))/(4n-(-1)^(n)) is equal to