In parts $($a$)-($d$),$ find the values of the sums in terms of n$.$ In part $($e$),$ evaluate the limit of the sum from part $($d$).$

$$k$=1$nk$=$

n$($n$+1)2$

$$k$=1$nkn$2=$

n$($n$+1)2$

$$k$=1$n$7$n$=$

$7$

$$k$=1$n$(6$kn$27$n$)=$

$3$n$2+3$n

$$ limn$$$($k$=1$n$(6$kn$27$n$))=$