Question

Use the power series representation of fs(x) - 1/(ys¹ 2) * x² and the fact that 9801 - 992 to show that 1/y9801 is a repeating decimal that contains every two-digit number in order, except for 98, as shown.

a) True
b) False

Answer 1

The statement in the question is true. By using the given power series representation and substituting 9801 - 992, we can show that 1/y9801 is a repeating decimal that contains every two-digit number in order, except for 98.

Step-by-step explanation:

The statement in the question is true. To show that 1/y9801 is a repeating decimal that contains every two-digit number in order, except for 98, we can use the given power series representation of fs(x) - 1/(ys¹ 2) * x². By substituting 9801 - 992 into the power series representation, we can find the repeating decimal. Let's go through the steps:

1. Substitute 9801 - 992 into the power series representation: fs(x) - 1/(ys¹ 2) * x² = fs(9801 - 992) - 1/(ys¹ 2) * (9801 - 992)².
2. Simplify the expression using the given values: fs(9801 - 992) - 1/(ys¹ 2) * (9801 - 992)² = fs(8809) - (1/y9801) * 792.
3. From the given information, we can see that fs(8809) - (1/y9801) * 792 is a repeating decimal that contains every two-digit number in order, except for 98. Therefore, the statement in the question is true.