计算调和级数和大于K的最小n值

///'根据题目已知条件可得：//nSn = 1 + 1/2 + 1/3 + ... + 1/n > K//n即 1/2 + 1/3 + ... + 1/n > K - 1//n设m = K - 1，则上式可改写为：//n1/2 + 1/3 + ... + 1/n > m//n根据调和级数的性质可知：//n1/2 + 1/3 + ... + 1/n 的和是无限逼近于ln(n)的，即：//n1/2 + 1/3 + ... + 1/n ≈ ln(n)//n因此，我们可以将上式改写为：//nln(n) > m//n再将等式两边取指数：//nn > e^m//n由此可得最小的n为e^m的上取整，即：//nn = ceil(e^m)//n其中，ceil表示向上取整函数。//n//n根据题目已知条件，K的取值范围是1<=K<=15，对应的m的取值范围是0<=m<=14。//n将每个m代入公式n = ceil(e^m)，计算得到对应的最小n，如下所示：//n//n当m=0时，n = ceil(e^0) = ceil(1) = 1//n当m=1时，n = ceil(e^1) = ceil(2.71828) = 3//n当m=2时，n = ceil(e^2) = ceil(7.38906) = 8//n当m=3时，n = ceil(e^3) = ceil(20.08554) = 21//n当m=4时，n = ceil(e^4) = ceil(54.59815) = 55//n当m=5时，n = ceil(e^5) = ceil(148.41316) = 149//n当m=6时，n = ceil(e^6) = ceil(403.42879) = 404//n当m=7时，n = ceil(e^7) = ceil(1096.63316) = 1097//n当m=8时，n = ceil(e^8) = ceil(2980.95799) = 2981//n当m=9时，n = ceil(e^9) = ceil(8103.08393) = 8104//n当m=10时，n = ceil(e^10) = ceil(22026.46579) = 22027//n当m=11时，n = ceil(e^11) = ceil(59874.14172) = 59875//n当m=12时，n = ceil(e^12) = ceil(162754.79142) = 162755//n当m=13时，n = ceil(e^13) = ceil(442413.39201) = 442414//n当m=14时，n = ceil(e^14) = ceil(1202604.28416) = 1202605//n//n综上所述，对于给定的整数K（1<=K<=15），要使得Sn>K，最小的n为：//n当K = 1时，n = 1//n当K = 2时，n = 3//n当K = 3时，n = 8//n当K = 4时，n = 21//n当K = 5时，n = 55//n当K = 6时，n = 149//n当K = 7时，n = 404//n当K = 8时，n = 1097//n当K = 9时，n = 2981//n当K = 10时，n = 8104//n当K = 11时，n = 22027//n当K = 12时，n = 59875//n当K = 13时，n = 162755//n当K = 14时，n = 442414//n当K = 15时，n = 1202605//n///