Find the value of b for which 1+e^b+e^2b+e^3b+...=9
Question
Answer:
this is a geometric series, let r=e^b then we have 1+r+r^2+r^3+....=9
1/(1-r)=9
1-r=(1/9)
r=1-(1/9)
r=8/9
e^b=8/9 take ln of both sides
ln(e^b)=8/9 ln(x^y)=y*ln(x) and ln(e)=1 so
b*ln(e)=b=ln(8/9)
thus
b=ln(8/9)
solved
general
5 months ago
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