Answer:
Sum = 551/999
Where a = 551 and b = 999
The two integers are 551 and 999
Step-by-step explanation:
Given
Decimal = 0.551
Ratio = 1/1000
By repeating the decimal, we can write;
0.551 -bar = 0.551551551.....
0.551551551..... = 0.551 + 0.000551 + 0.000000551 + ....
= 551/1000 + 551/1000000 + 551/1000000000 + ......
= 551/10³ + 551/10^6 + 551/10^9 + .....
= n=0 Σ∝(551/10³)(1/10³)^n
Hence, the infinite geometrc series is Σ(551/10³)(1/10³)^n for n = 0 to
∝
Given the ratio of 1/1000
Let r = 1/1000
r = 1/10³
a = 551/10³
The sum is defined as follows;
a/(1-r)
Sum = 551/10³ / (1 - 1/10³)
Sum = 551/1000 ÷ 999/1000
Sum = 551/999
So, a/b = 551/999
Where a = 551 and b = 999
The two integers are 551 and 999
