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Formulas for binomial series: (1-x)^r and sum{from 0 to n}(r k)(x)^k

sqrt(35) = sqrt(35*36/36) = 6*sqrt(35/36) = 6*sqrt(1-(1/36))

Now it looks more like the binomial series formula:

let r = 1/2 because of the radical and x = 1/36

6*[1-(1/36)]^(1/2) and use the second formula to expand:

6* sum{from 0 to n}(1/2 k)(1/36)^k

I did from k=0 to k=5:

= 6[1-(1/2)*(1/36)+(1/8)*(1/36)^2-(1/16)*(1/36)^3+(1/32)*(1/36)^4-(1/64)*(1/36)^5+....]

But I didn't get close enough with only 5 terms. First I used 4 terms beacause (1/32)*(1/36)^4 gave me 1.9*10^(-8) which I thought would be enough terms needed for an accuracy of 10^(-7) but wasn't.

I eventually got 6[0.98620624] = 5.917237444

and the actual sqrt(35) = 5.916079783

+- 0.001 and I need +- 0.0000001

My professor didn't teach us to use the alternating series estimation theorem which I though would help me find how many n terms I would need to use but I don't understand. Please help. I think I'm on the right track I'm just not quite there.

Thanks,

Sami