If N(n)=n _ r=1 ²⁰²³ (n^2-r^2 )(n>2023) , then ^N C_ N-1 when n=2024 is

Step-by-step solution

N(n)=n _ r=1 ²⁰²³ (n^2-r^2 )=n [ _ r=1 ²⁰²³(n-r) ] [ _ r=1 ²⁰²³(n+r) ] but when n =2024 ( given) aligned & N(2024)=2024[(2023)(2022)(2021) 3.2 .1] & [(2025)(2026) (4046)(4047)] & aligned Now rearranging above we get, aligned & N(2024)=(4047)(4026) (2025)(2024)(2023) 3.2 .1 & =(4047) ! aligned but we have to find ^N C_ N-1 when n=2024 Now ^N C_ N-1 = N ! (N-1) !(N-(N-1)) ! = N(N-1) ! (N-1) ! 1 ! aligned & ^N C_ N-1 =N & ^N C_ N-1 =(4047) ! when n=2024 aligned