On May 13, 7:49=A0pm, "Jim Dars" <jim-d...@[EMAIL PROTECTED]
> wrote:
> Hi All,
>
> Find y:
>
> Given: =A0g =3D a googolplex - 1
> =A0 =A0 =A0 =A0 =A0 =A0 =A0y =3D the largest number smaller than g such
th=
at
>
> =A0 =A0Sum(i =3D y to g) =A01/i =A0>=3D 1
>
> If you can't, can you recommend a good estimate of y?
>
> Best wishes, Jim
The obvious tack is to approximate the sum
by an integral:
SUM 1/k FOR k =3D y to g
is approximately INTEGRAL 1/x dx FROM x =3D y to g+1
or ln(googolplex) - ln(y). Because the integral
is a lower bound on the sum, we can infer a lower
bound for y:
y > exp(ln(googolplex) - 1) =3D googolplex/e
A tighter estimate can be given by bringing Euler's
gamma constant into the picture.
regards, chip
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