A. Little Pony and Expected Maximum

http://codeforces.com/problemset/problem/453/A

453A.py

@@ -0,0 +1,22 @@
+"""
+    http://codeforces.com/problemset/problem/453/A
+    the root problem: number of array A[n] of positive number that max(Ai) = x
+    
+      C(1,n)*(x-1)^(n-1) + C(2,n)*(x-1)^(n-2) + ...
+    = x^n - (x-1)^n
+    
+    E = sum(i*(i^n-(i-1)^n)/m^n
+      = sum(i*((i/m)^n - [(i-1)/m]^n)
+
+"""
+def power(a,n):
+    if n == 1: return a
+    x = power(a,n/2)
+    if n%2==0:
+        return x*x
+    else:
+        return x*x*a
+
+m,n = map(int, raw_input().split())
+result = sum(i * (power(i/1./m,n) - power((i-1)/1./m,n)) for i in range(1,m+1))
+print result