Which of the following assertions is true for the given sequences? 1)Double exponent: use braces to clarifyDouble exponent: use braces to clarify converges 2){n+12n+3} diverges 3){−1+2(−1)n} diverges 4){nsin⁡1n} converges 5)None of these

Question

Which of the following assertions is true for the given sequences?     1)Double exponent: use braces to clarifyDouble exponent: use braces to clarify converges    2){n+12n+3} diverges    3){−1+2(−1)n} diverges    4){nsin⁡1n} converges    5)None of these

Rylee Marshall · Accepted Answer

True sequences: 2) n+12n+3 diverges 3) −1+2(−1)n diverges an=n+12n+3 Now, check convergence of ∑n=0∞an ∑n=0∞n+12n+3 Apply series Divergence test =diverges Thus, ∑n=0∞n+12n+3: diverges  This is a true sequence 3)an=−1+2(−1)n Check the convergence of ∑n=0∞an ∑n=0∞−1+2(−1)n Apply Divergence test =diverges Thus, ∑n=0∞a−1+2(−1)n:÷er≥s. Thus, this is a true sequence.

Which of the following assertions is true for the given

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