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Apakah Deret berikut Konvergen atau Divergen? (Bobot 20) a). sum_(n=1)^(oo)(1)/(n^(1,500)) b). sum_(n=1)^(oo)(1)/((1)/(n^(4)))

55. Apakah Deret berikut Konvergen atau Divergen? (Bobot 2020)\newlinea). ∑n=1∞1n1,500 \sum_{n=1}^{\infty} \frac{1}{n^{1,500}} \newlineb). ∑n=1∞11n4 \sum_{n=1}^{\infty} \frac{1}{\frac{1}{n^{4}}}

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Q. 55. Apakah Deret berikut Konvergen atau Divergen? (Bobot 2020)\newlinea). ∑n=1∞1n1,500 \sum_{n=1}^{\infty} \frac{1}{n^{1,500}} \newlineb). ∑n=1∞11n4 \sum_{n=1}^{\infty} \frac{1}{\frac{1}{n^{4}}}
  1. Check Convergence: a) Check if the series ∑n=1∞1n1.500\sum_{n=1}^{\infty}\frac{1}{n^{1.500}} is convergent using the p-series test where p>1p > 1 for convergence.
  2. Apply p-series test: Since p=1.500p = 1.500 which is greater than 11, the series converges by the p-series test.
  3. Rewrite series: b) Rewrite the series ∑n=1∞1(1n4)\sum_{n=1}^{\infty}\frac{1}{\left(\frac{1}{n^{4}}\right)} as ∑n=1∞n4\sum_{n=1}^{\infty}n^{4}.
  4. Apply p-series test: Apply the p-series test again, where p=4p = 4 which is greater than 11.
  5. Convergence by p-series test: Since p=4p = 4 is greater than 11, the series converges by the p-series test.

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