Question

* Let $h_n$ denote the number of regions into which a convex polygonal region with $n + 2$ sides is divided by its diagonals, assuming no three diagonals have a common point. Define $h_0 = 0$. Show that $h_n = h_{n-1} + inom{n+1}{3} + n$, ($n ge 1)$.

          * Let $h_n$ denote the number of regions into which a convex polygonal region with $n + 2$ sides is divided by its diagonals, assuming no three diagonals have a common point. Define $h_0 = 0$. Show that 
$h_n = h_{n-1} + inom{n+1}{3} + n$, ($n ge 1)$.

* Let hn denote the number of regions into which a convex polygonal region with n + 2 sides is divided by its diagonals, assuming no three diagonals have a common point. Define h0 = 0. Show that
hn = hn-1 + inomn+13 + n, (n ge 1).

Added by Rachael C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/06/2022

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Step 1: Let's denote hn as the number of regions an 8 convex polygonal region with n + 2 sides is divided into by its diagonals. Show more…

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Let hn denote the number of regions into which a convex polygonal region with n + 2 sides is divided by its diagonals, assuming no three diagonals have a common point. Define h0 = 0. Show that hn = hn-1 + (n+1 choose 3) + n, (n >= 1).