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。
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