Question

Round to the nearest hundredth (Geometric Series problem)

Answer 1

Answer:

15.98

Step-by-step explanation:

∑₁¹⁰ $8(\frac{1}{4} )^{n-1}$

$=8[1+\frac{1}{4} +\frac{1}{16} + ........ +t_{10}]$

We have to use the formula of sum of a G.P. series with common ratio r < 1.

If the first term is a, the common ratio is r and the number of terms is n then the sum [a + ar + ar² + ar³ + ......... up to n terms] is given by  

$[a \times\frac{1-r^{n} }{1-r}]$

$= 8[1 \times \frac{1-\frac{1}{2^{10} } }{1-\frac{1}{2} } ]$

$= 15.98$ (Answer)