Question 750011
{{{sum(3(0.4)^(n-1),n=1,infinity)}}}

{{{sum(3(4/10)^(n-1),n=1,infinity)}}}


{{{sum(3(2/5)^(n-1),n=1,infinity)}}}

use partial fractions

{{{sum(3(2/5)^(n-1),n=1,m)=(2^m-5^m)(-5^(1-m))=-5^m*((2^m/5^m-1))(-5^(1-m))=-5*((2/5)^m-1))}}}

if {{{m}}} -> {{{infinity}}}, then {{{(2/5)^m=0}}}; so, we will have

{{{sum(3(2/5)^(n-1),n=1,m)=-5*(0-1)=-5*0-5*(-1)=5}}}