Answer:
the sum of the first 10 terms is: 79.921875
Step-by-step explanation:
Notice that this is a geometric series, of the sequence that has "40" as the first term, and the following ones are obtained by multiplying by the common ratio "1/2".
So the common ratio [tex]r=\frac{1}{2}[/tex], and the first term [tex]a_1=40[/tex], then, recalling the formula for the partial sum of n terms of a geometric sequence:
[tex]S_n=\frac{a_1\,(1-r^n)}{1-r}[/tex]
we can find the sum of this sequence's first 10 terms (n=10):
[tex]S_n=\frac{a_1\,(1-r^n)}{1-r} \\S_{10}=\frac{40\,(1-(\frac{1}{2}) ^{10})}{1-\frac{1}{2} } \\S_{10}=79.921875[/tex]
