Question

The two convergent subsequences of the sequence (-1)^3n+2 is

Answer 1

Answer:

3n +2 The two convergent subsequences of the sequence (-1)"" + 2 is a) x, = (-1)" +2 and xn1 =[(-1)] + b) xın =(-1)º+2 and x2n-1 = | c) Xzn =(-1)" +2 and Xn1 = (-1)2n+2 + 2 d) 4n = (-1)" +2 and X2n-1 =(-1)}" + 2 2n+1 +2

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Answer 2

Answer:

Two convergent subsequence are {1,1,1…} and {-1,-1,-1,…}.

Step-by-step explanation:

Given:- $( -1 )^{3n+2}$

To Find:- Two convergent subsequences of the above sequence

Solution:-

3n + 2 = ( 2(n+1) + n )

So, $( -1 )^{3n+2}$ = $( -1 )^{(2(n+1)+n)}$

                    = $( -1 )^{2(n+1)} (-1)^n$

                    = $( 1 )^{n+1} (-1)^n$

                    = $( 1 )^{n} (1)^1(-1)^n$

                    = $( -1 )^{n}$

Hence,  two convergent subsequence will be {1,1,1…} and {-1,-1,-1,…}.

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