Answer:
15.98
Step-by-step explanation:
∑₁¹⁰ [tex]8(\frac{1}{4} )^{n-1}[/tex]
[tex]=8[1+\frac{1}{4} +\frac{1}{16} + ........ +t_{10}][/tex]
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
[tex][a \times\frac{1-r^{n} }{1-r}][/tex]
[tex]= 8[1 \times \frac{1-\frac{1}{2^{10} } }{1-\frac{1}{2} } ][/tex]
[tex]= 15.98[/tex] (Answer)
