Sum of Geometric Progression

Author: Shikha-code36

README.md

@@ -4,6 +4,7 @@ Data Structures and Algorithms implementation in Python.
 
 ### Topics covered:
 - [x] [Recursion](Recursion)
-    - [x] [Basic-Problems](Recursion/Basic-Problems)
+    - [x] [Basic Problems](Recursion/Basic-Problems)
         - [x] [Factorial](Recursion/Basic-Problems/factorial.py)
-        - [x] [Fibonacci](Recursion/Basic-Problems/fibonacci.py)
+        - [x] [Fibonacci](Recursion/Basic-Problems/fibonacci.py)
+        - [x] [Sum of Geometric Progression](Recursion/Basic-Problems/GP.py)

Recursion/Basic-Problems/GP.py

@@ -0,0 +1,27 @@
+'''
+                                    Geometric Progression
+The nth term of a GP series is Tn = arn-1, where a = first term and r = common ratio = Tn/Tn-1) . The sum of infinite terms of a GP series S∞= a/(1-r) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.
+
+
+Given an integer N, we need to find the geometric sum of the following series using recursion. 
+
+1 + 1/3 + 1/9 + 1/27 + … + 1/(3^n) 
+
+Input N = 5 
+Output: 1.49794
+
+Input: N = 7
+Output: 1.49977
+
+Approach:
+We will calculate the last term and call recursion on the remaining n-1 terms each time. The final sum returned is the result.
+'''
+
+def geo_sum(n):
+    if n==0:
+        return 1
+
+    sum = 1/pow(2,n) + geo_sum(n-1)
+    return sum
+
+print(geo_sum(8)) #1.499923792104862