added series hw

Author: rajban1918

Students/ralbright/Session02/series.py

@@ -0,0 +1,56 @@
+def fib(n):
+    """Return the nth  value in the fibonacci function, which is a recursive function. """
+    if n == 0:
+        return 0
+    elif n == 1:   
+        return 1           
+    else:                      
+        return fib(n-1) + fib(n-2)
+
+# print fib(7)
+
+
+def lucas(n):
+    """Return the nth value in the Lucas function, which is also a recursive function but starts with 2 and 1 rather than 0 and 1"""
+    if n == 0:
+        return 2
+    elif n == 1:
+        return 1
+    else:
+        return lucas(n-1) + lucas(n-2)
+# print lucas (2)
+# print lucas (7)
+
+
+def sum_series(n, x=0,y=1):
+    """ Return the nth value of a recursive function. There are two optional parameters, x and y.
+        x is the 0th value and y is the 1st value.
+
+        When x = 0 and y = 1, the result is the fibbonacci sequence
+        When x = 2 and y = 1, the result is the lucas sequence
+        When x  and y are other values, there are different sequences
+    """
+    if n == 0:
+        return x
+    elif n == 1:
+        return y
+    else:
+        return sum_series(n-1, x, y) + sum_series(n-2, x, y) # it took me a while to figure out why it was going back to fibbonacci 
+                                                                                        # even when x =2, of course have to re-add x and y in the else part!!!
+
+# print sum_series(0,2)
+# print sum_series(1,0,4)
+# print sum_series(2)
+# print sum_series(7)
+# print sum_series(7,2)
+# print sum_series(7,3,1)
+
+
+if __name__ == "__main__":
+    assert fib(7) == 13
+    assert lucas (7) == 29
+    assert sum_series(7) == 13
+    assert sum_series(7,2) == 29
+    assert sum_series(7,3) == 37
+
+print "all good here"