Test the series:
n=1 ∑∞ (-1)n-1 [Sin(nx)]/n√n
for absolute and conditional convergence.
Then
The series ∑n=1∞1nn\displaystyle\sum_{n=1}^{\infin}\dfrac{1}{n\sqrt{n}}n=1∑∞nn1 converges as ppp -series with p=32>1.p=\dfrac{3}{2}>1.p=23>1.
Therefore the series ∑n=1∞(−1)nsin[nx]nn\displaystyle\sum_{n=1}^{\infin}\dfrac{(-1)^n\sin[nx]}{n\sqrt{n}}n=1∑∞nn(−1)nsin[nx] converges absolutely by the Comparison Test, for x∈R.x\in\R.x∈R.
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Dear Rajkumar, please use the panel for submitting a new question.
Test the following series for convergence ∑ n=1 ∞ [✓n^4+9 -✓n^4-9]
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Dear Rajkumar, please use the panel for submitting a new question.
Test the following series for convergence ∑ n=1 ∞ [✓n^4+9 -✓n^4-9]
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