Geometric series

How many terms of the geometric series 8+4+2+1+0.5+... must be taken for the sum to get within 10 to the power minus 4 of its sum to infinity?

Correct answer:

n =  14

Step-by-step explanation:

a1=8 a2=4  q=a2/a1=4/8=21=0.5  q<1  qn < 104  n log q > 4  n1=4/log10(q)=4/log100.513.2877 n=n1=13.2877=14

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