Real life challenge

Distance he will travel is D= (20+(20/2)+(20/4)+(20/8)+.... ) Factor out 20 D=20(1+(1/2)+(1/4)+(1/8)+...)
D=20(1+s) were s is the famous geometric series like from zenos paradox and is known to equal 1 so then D=20(1+1)=40 meters So as the amount of time he travels approaches infinity he will reach 40 meters and be 1 meter short of his destination

This was very poorly worded. But if he walks half the distance to school, he will never reach it blah blah blah

The distance covered are equivalent to the sum: $20 +10 +5 + 2.5 + 1.25 + ... = \frac{20}{1-\frac{1}{2}} = 40$ However this would take infinitely long, which is impossible so he will never reach the school (although he will get very close)

If you know Radioactive Decay....you can compare this situation here with radioactive decay.

Use the formula for geometric progressions $\frac {1}{1-k}$ with ratio $k=\frac {1}{2}$ . Since the first term is 20 we have $20 \times \frac {1}{1-k}$ which is equal to 40<41. He won't never reach his school.

the asymptote or summation ends at 40 so he'll never get there...

I've answered several of these, yet the answer always assumes a problem that does not exist. Assuming that Aman has arms, he will end up infinitesimally close to the school, enough where he could simply reach out and touch it. This distance would be attainable within ten minutes of walking, as he would be within a third of a meter from the door, which is within range for any child old enough to walk to school alone.

This is not Zeno's paradox though. since here there is a clear deceleration. Rather the only difference between this and a simple V1 = 20m/m (meters per minute) a = -10m/m^2 is that the acceleration is non linear. the rate of deceleration or the jolt, also has a decreasing trend. where J = 5m/m^3 except jolt also had a decreasing trend. simply put the limit of travel is 20m

But this is not the same as zero's paradox where the velocity is the same through out, yet the reference frame is cut to make a paradox out of a non paradoxical situation. Essentially inorder to move 40m you first must move an infinite amount of distances with length 0, which turns out to be easy.

If he starts walking,infinity will have to pass(which of course is impossible) before he reaches his school.So the answer is $\boxed{Aman\;will\;never\;reach\;his\;school}$ .I thought he,d have to walk for infinity.Which is not possible.I literally did not use any math.

He never reach school Because in first min 4m And at the 2nd min he covers 2m and 3Rd min 1m and goes on. It never comes to 50