Answer:
5.33
Step-by-step explanation:
move the 4 out of the summation because just a constant multiplier
4 *sum from 1 to 10 for (1/4)^(n-1) [sorry i don't know how to write sums using latex)
The formula for the geometric sum is :
First term*(1-multiplier^n)/(1-multiplier), formally [tex]\frac{a_1(1-r^n)}{1-r}[/tex]
Here multiplier is 1/4
First term is (1/4)^(1-1) = 1
Thus the value of sum is [tex]1*(1-(1/4)^1^0)/(1-1/4)[/tex]which equals [tex](1- (1/4)^1^0)*4/3[/tex]
We factored out 4 so its [tex]4*(1-(1/4)^1^0)*4/3[/tex] which is [tex]16/3 * (1- (1/4)^1^0)[/tex]
This equals 5.333328247 which is 5.33 to the nearest hundredth
