Which of the following statements correctly explains why the error in approximating the sum of the alternating series ∑k=1∞(−1)kbk \displaystyle \sum_{k=1}^{\infty} (-1)^k b_k , where bk b_k is positive, nonincreasing, and tends to zero, is less than or equal to the magnitude of the first omitted term after M M terms?

The error is less than or equal to bM+1b_{M+1} because the terms decrease and alternate in sign.

The error is exactly zero for all alternating series.

The error is always less than the sum of all omitted terms.

The error is greater than the first omitted term because the series diverges.

Which of the following statements correctly explains why the erro...

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