Please start a new thread instead of tacking on to an earlier question for new problems. That way they get the attention they deserve.

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11

21

1211

111221

-->What goes here?

Hope its not too easy

]]>My method may be the same what bobbym says, but I approached by observing that the series is

]]>Start by forming the power series:

This will equal the terms of Tony's series if x=1. There are differences of 4 and 2 in the exponents. The expansion:

Has exponents that differ by 2.

Has exponents that differ by 4. To get differences of 4 and 2 we use a

This has the required differences of 4 then 2 in the exponents.

Now I tried to use integration, differentiation or multiplication by x on (B)

to make it look like series (A).

I couldn't. So I tried

This one doesn't have the required 4,2 difference in the exponents so it can't be right.

When I tried:

This looks good. Integrate this series and you get

(C) is series (A). So we have:

Now we need the integral.

with x=1

]]>tony123 wrote:You made a little mistake, mate. I think you want to find

no jane

]]>

You made a little mistake, mate. I think you want to find

The Maclaurin series for

isAlso

Hence

]]>I haven't solved it yet, but it's fairly easy to see that it's somewhere between 0.8 and 1.

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