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777dan777 [17]
4 years ago
8

Find the value of b for which 1+e^b+e^2b+e^3b+...=9

Mathematics
1 answer:
KonstantinChe [14]4 years ago
5 0
This is a geometric series, let r=e^b then we have 
<span>1+r+r^2+r^3+....=9 </span>
<span>1/(1-r)=9 </span>
<span>1-r=(1/9) </span>
<span>r=1-(1/9) </span>
<span>r=8/9 </span>
<span>e^b=8/9 take ln of both sides </span>
<span>ln(e^b)=8/9 ln(x^y)=y*ln(x) and ln(e)=1 so </span>
<span>b*ln(e)=b=ln(8/9) </span>
<span>thus </span>
<span>b=ln(8/9)</span>
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