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If a function f satisfies f( ~m + n )=f( ~m )+f( n ) for all m , n N and f(1)=1 , then the largest natural number such that _ k=1 ²⁰²² f( +k) (2022)^2 is equal to _________

Correct answer

0

Step-by-step solution

aligned & f ( m + n )= f ( m )+ f ( n ) & f ( x )= kx & f (1)=1 & k =1 & f ( x )= x aligned Now _ k =1 ²⁰²² f ( + k ) (2022)^2 aligned & _ k =1 ²⁰²²( + k ) (2022)^2 & 2022 + 2022 2023 2 (2022)^2 aligned aligned & 2022- 2023 2 & 1010.5 aligned largest natural no. is 1010 .

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