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SVETLANKA909090 [29]
4 years ago
9

Find the sum of the convergent series. 9 + 0.9 + 0.09 + 0.009 + . .

Mathematics
1 answer:
Papessa [141]4 years ago
8 0

Try this solution:

1. Note, that 9*0.1=0.9; 0.9*0.1=0.09; 0.09*0.1=0.009, etc.

It means, the gives series is geometric sequence, where a₁=9, q=0.1.

2. Using a₁=9 and q=0,1 it is possible to calculate the sum of this sequence:

S=\frac{a_1}{1-q}; \ S=\frac{9}{1-0.1}=\frac{9}{0.9}=10.


answer: 10

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Step-by-step explanation:

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6) ?

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