The Very Long Sequence!
What is
1 0 0 0 0 ⋅ 9 9 9 8 ⋅ 9 9 9 6 ⋅ 9 9 9 4 ⋅ 9 9 9 2 ⋅ 9 9 9 0 ⋅ . . ⋅ − 9 9 9 0 ⋅ − 9 9 9 2 ⋅ − 9 9 9 4 ⋅ − 9 9 9 6 ⋅ 9 9 9 8 ⋅ 1 0 0 0 0
The answer is 0.
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2 solutions
A previous version of this problem, as stated by @Pi Han Goh's comment (you can access it by clicking on "View reports" in the orange box) multiplies the even natural numbers from 1 0 0 0 0 to − ∞ . Since in that version of the problem, the numbers extend to − ∞ , the problem can be reduced to multiplying 0 ∗ − ∞ which is an undefined result.
Note: The problem has since been altered into its present wording.
This question is phrased quite unclearly, so the answer cannot be verified until the author does. However, if the author means to "find the product of the even integers", we can solve the question as follows:
Since 0 is an even integer, the product of 0 and ( 1 0 0 0 0 ⋅ 9 9 9 8 ⋅ 9 9 9 6 ) ⋯ ⋅ ( 2 ⋅ 0 ⋅ − 2 ) ⋯ ( − 9 9 9 8 ⋅ − 1 0 0 0 0 ⋅ − 1 0 0 0 2 ) ⋯ = 0 , since 0 ⋅ n = 0 is an identity and holds for all values of n .
Therefore, combining these two facts gives the answer 0 .
Since Eventually the numbers will go down to 0, the answer is 0