Question

For the series below calculate the sum of the first 3 terms, S₃ and find a bound for the error. Make sure to include at least several decimals for accuracy when the problem is graded.

∑[n=0 to [infinity]] ((-1)ⁿ600 / n⁰.⁶), S₃ =__

Answer 1

The sum of the first 3 terms of the given series is 600 + (-600 / 1.1486983549970353) + (600 / 1.6523684777422858). The error bound is calculated using the absolute value of the first neglected term: E ≤ Absolute value of ((-1)³600 / 3⁰.⁶), which is approximately 1242.4254691861532.

Step-by-step explanation:

To find the sum of the first 3 terms of the series, we need to substitute the values of n in the given expression and then add them up.

S₃ = ((-1)⁰600 / 0⁰.⁶) + ((-1)¹600 / 1⁰.⁶) + ((-1)²600 / 2⁰.⁶)

Simplifying this, we get:

S₃ = 600 + (-600 / 1.1486983549970353) + (600 / 1.6523684777422858)

Now, let's find a bound for the error. Since the series is an alternating series, we can use the Alternating Series Estimation Theorem. The error bound, E, can be found using the absolute value of the first neglected term:

E ≤ Absolute value of ((-1)³600 / 3⁰.⁶)

Calculating this, we get:

E ≤ 1242.4254691861532