What is alternating series remainder Theorem?

What is alternating series remainder Theorem?

Mathwords: Alternating Series Remainder. A quantity that measures how accurately the nth partial sum of an alternating series estimates the sum of the series. If an alternating series is not convergent then the remainder is not a finite number.

How do you find the error in a series?

00001 value is called the remainder, or error, of the series, and it tells you how close your estimate is to the real sum. Estimate the total sum by calculating a partial sum for the series. Use the comparison test to say whether the series converges or diverges. Use the integral test to solve for the remainder.

What is the P test for series?

Theorem 7 (p-series). A p-series ∑ 1 np converges if and only if p > 1. Proof. If p ≤ 1, the series diverges by comparing it with the harmonic series which we already know diverges.

Can an alternating series diverge?

The alternating series test can only tell you that an alternating series itself converges. Always check the nth term first because if it doesn’t converge to zero, you’re done — the alternating series and the positive series will both diverge.

What is the remainder of 1 divided by 3?

When 1 is divided by 3, remainder is 1.

What is a remainder of a number?

In mathematics, the remainder is the amount “left over” after performing some computation. In arithmetic, the remainder is the integer “left over” after dividing one integer by another to produce an integer quotient (integer division).

What is the remainder of an alternating series?

Alternating Series Remainder. A quantity that measures how accurately the nth partial sum of an alternating series estimates the sum of the series. If an alternating series is not convergent then the remainder is not a finite number. Consider the following alternating series (where a k > 0 for all k) and/or its equivalents.

What is the sum of this alternating series?

An alternating sum is a series of real numbers in which the terms alternate sign. For example, the alternating harmonic series is. Alternating sums also arise in other cases. For instance, the divisibility rule for 11 is to take the alternating sum of the digits of the integer in question and check if the result is divisble by 11.

When does an alternating series converge?

An alternating series converges if each term is numerically equal to or less than the preceding and if the n-th term approaches zero as n increases without limit. This is a sufficient, but not a necessary set of conditions — the term-by-term sum of any two convergent series converges and,…

What is alternating series error bound?

Alternating Series – Error Bound. Series. Definition, using the sequence of partial sums and the sequence of partial absolute sums. Absolutely convergent and conditionally convergent series are defined, with examples of the harmonic and alternating harmonic series.