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Classify the series. ∑n=134(n+2)3 \sum_{n = 1}^{34} (n + 2)^3 \newlineRadio Choices:\newline[A]infinite\text{[A]infinite}\newline[B]finite\text{[B]finite}

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Q. Classify the series. ∑n=134(n+2)3 \sum_{n = 1}^{34} (n + 2)^3 \newlineRadio Choices:\newline[A]infinite\text{[A]infinite}\newline[B]finite\text{[B]finite}
  1. Upper Limit Analysis: Look at the upper limit of the series, which is 3434. Since it's a specific number, not infinity, the series has a finite number of terms.
  2. Lower Limit Analysis: Check the lower limit of the series, which is 11. This confirms that the series starts at n=1n=1 and ends at n=34n=34, which is a total of 3434 terms.
  3. Series Finiteness: Since both the upper and lower limits are finite numbers, the series ∑n=134(n+2)3\sum_{n = 1}^{34} (n + 2)^3 is a finite series.

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