※ 引述《changkh (月光華華)》之銘言： : 最近我朋友碰上了一題數學題不知道怎麼解，不知道有沒有人學過呢？ : In the zipper model for the helix-coil transition, the partition : function Q is give by: : N : Q= 1 + sigma * sum (N - i + 1) s^i : i=1 : sum is summation. : Where N is the number of residues in the chain. : a) using the fact that : N : sum s^i = (s^(N+1) - S) / s - 1 : i=1 : show that the partition function in zipper model can be : evaluated to give: : Q= 1 + (sigma * s) * (s^(N+1) - (N+1)s + N) / (s - 1)^2 : b) show that the average fraction of helical residue, theta, : can be obtained from : theta = 1 / N * (ln Q對ln s的偏微分) : 謝謝啦。 其實後來我也算出了a) 這題重點是 N sum i*s^i怎麼算 i=1 我的算法是設 N N s^(N+1) - s I=sum i*s^i 又令 J=sum s^i = ------------- i=1 i=1 s - 1 I = s + 2s^2 + 3s^3 + ... + (N-1)s^(N-1) + Ns^N J= s + s^2 + s^3 + ... + S^(N-1) + s^N 則I-J= 0 + s^2 + 2s^3 + ... + (N-2)s^(N-1) + (N-1)s^N = I*s-Ns^(N+1) 所以I-J= Is - Ns^(N+1) 化簡可得I --

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