Write the first four terms of the following sequences. If the sequence appears to converge, make a c

Pitrellais

Pitrellais

Answered question

2022-05-28

Write the first four terms of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why.
a n = 1 10 n ; n = 1 , 2 , 3 , . . .

Answer & Explanation

Krish Finley

Krish Finley

Beginner2022-05-29Added 14 answers

Given:
a n = 1 10 n ; n = 1 , 2 , 3 , . . .

a 1 = 1 10 1
a 1 = 1 1 10 = 9 10 = 0.9
a 2 = 1 10 2
a 2 = 1 1 100 = 99 100 = 0.99
a 3 = 1 10 3
a 3 = 1 1 1000 = 999 1000 = 0.999

The value of n goes to infinity, and the terms appear to increase and approach 1.
Thus, the conjecture is lim n a n = 1

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