Robert wants to know his body mass to arbitrary precision. He has a big balancing scale that works perfectly, an unlimited collection of 1 -kg weights, and nine each of 0.1 -kg, 0.01 -kg, 0.001 -kg, and so on weights. Assuming the scale is big enough, can he do this? What does this have to do with infinite series?
Answers
Given : Robert wants to know his body mass to arbitrary precision. He has a big balancing scale that works perfectly, an unlimited collection of 1 -kg weights, and nine each of 0.1 -kg, 0.01 -kg, 0.001 -kg, and so on weights
To find : Can Robert weigh his body mass to arbitrary precision
Solution:
He has unlimited collection of 1 -kg weights
hence weights in integers can be measured for any value
Now to measure weight between two integers
Robert has
0.1 kg , 0.01 kg , 0.001 kg . ........
this is an infinite GP
a = 0.1 kg
r = 1/10
Sum = a/(1 - r) = 0.1/( 1 - 1/10) = 1/9 kg
& its given he has 9 of each weight
then total = 9 * 1/9 = 1 kg
So his all weight can weigh a total of 1 kg
Hence he can measure each value between integer using those weights
Yes , Robert can weight his body mass to arbitrary precision.
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