Solve sum no 23 23 Prove a polygon of n sides has n(n-3)2 diagonals n 3 - Maths - Principle of Mathematical Induction

Question

Solve sum no 23

23 Prove a polygon of n sides has n ( n - 3 ) 2   d i a g o n
a l s   n > 3

Shruti Tyagi · Accepted Answer

Dear Student,

Let dn be the number of diagonals of a polygon
 Assuming that the number of diagonals of a n-polygon is n(n−3)2Сonsider (n+1) polygon A1, A2…
An+1Under the assumption the number of diagonals of n-polygon A1, A2…An is nn-32, Besides there are n−1diagonals An+1A2, An+1 A3,…,An+1 An−1 and A1An for n+1−polygon A1A2…An+1Therefore the number of diagonals of (n+1)-polygon A1, A2…An+1 equal to dn+1=n(n−3)2+n−1=n2−3n+2n−22=(n+1)(n+1)−32

Regards,

Solve sum no 23 23. Prove a polygon of n sides has n ( n - 3 ) 2 d i a g o n a l s . n > 3 .

Solve sum no 23

23. Prove a polygon of n sides has $\frac{n (n - 3)}{2} d i a g o n a l s . n > 3 .$