Consider the signal

g$[$n$]=$

$1$

k$=2$

kf $[$k $$ n$]$

where f $[$n$]=2$n $1.$ Compute the values of the following expressions.There should be no

summations in your final expression. Recall the following geometric series summations.

$\backslash$infty $$

k$=0$

ark $=$ a

$1$ r $,$ if $|$r$|<1$

$\backslash$infty $$

k$=1$

akr$($k$1)=$ a

$(1$ r$)2,$ if $|$r$|<1.$

$($i$)$ Calculate the explicit expression of g$[$n$],$ i$.$e$.,$ write down the expression of g$[$n$]$ where

the only variable is n$.$

$4$

$($ii$)$ calculate g$[4]$

$5$

$($iii$)$ Calculate $2$

k$=\backslash$infty

$2$kg$[$k$].$