A sequence is defined by the recursive function
1 answer:
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Answer:
14/45
Step-by-step explanation:
So we have the fraction:
We can do this algebraically. Follow to following steps:
Let's let this number equal to n. Thus:
Since there is only 1 digit repeating, let's multiply everything by 10. So:
Now, subtract n from both sides:
On the left, substitute the number for n. On the right, combine like terms:
All of the 1s will cancel. So:
Subtract:
Divide both sides by 9:
Remove the decimal by multiplying both sides by 10:
Reduce:
And we're done!
Use a calculator to check: