Use the geometric sum formula to find out the value for this

Use the geometric sum formula to find out the value for this: 1 + 3 + 3^2 + 3^3 + 3^4 + ... + 3^15 Use the substitution method to find out the complexity of this function: T(n) = n^2 + 5 middot T(n/2)

Solution

2. To find the sum of a certain number of terms of Geometric Series :-

The Formula :- S(n) = a1(1-r^n)/1-r

where s(n) be the sum of n terms
a1 be the first term
r be the common ratio

Given :-

1 + 3 + 3^2 + 3^3 + 3^4 + ............ + 3^15

where a1=3
n=15
r=3

Therefore S(n) = a1 ( 1 - r^n ) / (1 - r)

S(15) = 3 ( 1 - 3^15 ) / (1-3).