Fix Exercise 3.9 solution (iamhectorotero#12)

Kacjer · Jun 15, 2020 · b78cc54 · b78cc54
1 parent fcc4b3b
commit b78cc54
Showing 1 changed file with 19 additions and 4 deletions.
diff --git a/Chapter 3/Chapter 3 Exercises.ipynb b/Chapter 3/Chapter 3 Exercises.ipynb
@@ -247,11 +247,26 @@
     "\n",
     "## Answer\n",
     "\\begin{equation*}\n",
-    "G_0 = 2 + 7 \\frac{1}{1 - \\gamma} = 72\n",
+    "G_0 = 2 + \\gamma\\ 7 + \\gamma^2\\ 7 + ... = 2 + \\gamma\\ ( \\sum_{k=0}^{\\infty} \\gamma^k\\ 7 ) = 2 + \\gamma\\ 7\\ ( \\sum_{k=0}^{\\infty} \\gamma^k) =  2 + \\gamma\\ 7\\ (\\frac{1}{1 - \\gamma}) = 2 + 0.9 \\times 7 \\times 10 = 65\n",
     "\\end{equation*}\n",
     "\\begin{equation*}\n",
-    "G_1 = 7 + 7 \\frac{1}{1 - \\gamma} = 77\n",
-    "\\end{equation*}"
+    "G_1 = 7 + \\gamma\\ 7 + \\gamma^2\\ 7 + ... = 7\\ ( \\sum_{k=0}^{\\infty} \\gamma^k) = 7 \\frac{1}{1 - \\gamma} = 70\n",
+    "\\end{equation*}\n",
+    "\n",
+    "This results fulfills:\n",
+    "\n",
+    "\\begin{equation*}\n",
+    "G_0 = R_1 + \\gamma G_1 = 2 + 0.9 \\times 70 = 65\n",
+    "\\end{equation*}\n",
+    "\n",
+    "This problem can also be solved through the equations below (note that G_2 = G_1 = G_n where n > 0):\n",
+    "\n",
+    "\\begin{equation*}\n",
+    "G_0 = R_1 + 0.9\\ G_1\n",
+    "\\end{equation*}\n",
+    "\\begin{equation*}\n",
+    "G_1 = R_2 + 0.9\\ G_1\n",
+    "\\end{equation*}\n"
    ]
   },
   {
@@ -432,7 +447,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.6"
   }
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  "nbformat": 4,