Identify the set as finite or infinite.
{1, 1/4, 1/16, 1/64, ...}
A. Finite
B. Infinite
Can someone explain this one for me?
Answer (3)
1 ; 4 1 ; 16 1 ; 64 1 ; ... a 1 = 4 1 − 1 1 = 4 0 1 = 1 1 = 1 a 2 = 4 2 − 1 1 = 4 1 1 = 4 1 a 3 = 4 3 − 1 1 = 4 2 1 = 16 1 a 4 = 4 4 − 1 1 = 4 3 1 = 64 1 ⋮ a n = 4 n − 1 1
n → ∞ lim 4 n − 1 1 = n → ∞ lim 4 n ⋅ 4 − 1 1 = n → ∞ lim 4 n ⋅ 4 1 1 = n → ∞ lim 4 n 4 = 0 A n s w er : A
Finite because the decimals end. If it was 1/3 then it would be infinite because the decimals would go on foreber
The set {1, 1/4, 1/16, 1/64, ...} is infinite because we can continue generating more terms indefinitely by increasing n. There is no limit to the number of terms we can create in this pattern. Thus, the correct answer is B. Infinite.
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