Binomial Sum

[man111]

If \displaystyle A = \sum_{r=0}^{24}\binom{100}{r}.\binom{100}{4r+2} and \displaystyle B = \sum_{r=1}^{25}\binom{200}{8r-6}

Then \displaystyle \frac{A}{B} =

[maxal]

See http://en.wikipedia.org/wiki/Series_multisection