Find the indicated sum Use the formula for the sum of the fi

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. sigma^5_i = 1 (2/3)^i + 1 sigma^5_i = 1 (2/3)^i + 1 = (Type an integer or a simplified fraction.)

Solution

Sum of n terms of geometric series: a1[ 1- r^n]/(1- r)

a1 = (2/3)^2 = 4/9 ; a2 = (2/3)^3 = 8/27

r = 4/9

So, Sum = (4/9)[ 1 - (4/9)^5]/[ 1- 4/9]

= (4/9)[58025]/9(5/9)

= (4/9)(58025)/5

= 232100/45

= 46420/9