What are the terms a_{0}, a_{1}, a_{2},\ and\ a_{3} of

ffortunyu

ffortunyu

Answered question

2021-12-06

What are the terms a0,a1,a2, and a3 of the sequence {an}, where an equals an=[n2]+[n2]?

Answer & Explanation

Xyle1991

Xyle1991

Beginner2021-12-07Added 15 answers

an=[n2]+[n2]
Ceiling function [x]: smallest integer that is greater than or equal to x.
Floor function [x]: largest integer that is less than or equal to x.
We need to determine a0,a1,a2, and a3.
We obtain these terms by evaluating the given formula at n=0,1,2,3:
a0=[02]+[02]=[0]+[0]=0+0=0
a1=[12]+[12]=0+1=1
a2=[22]+[22]=[1]+[1]=1+1=2
a3=[32]+[32]=1+2=3

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