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19 June, 21:51

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

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  1. 19 June, 22:17
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    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)
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