Understanding Infinity
What is the value of 1+ 1/2 + 1/4 + 1/8+ 1/16+ 1/32+ 1/64 +................ ∞ ? Is it = 2 or ≈(approximately) 2 ? I always thought it to be approximately equal to 2 Why ? Cause I assumed it to be something like 1.999999999...something.... which was being approximated to 2 due to paucity of space !! So with this flawed understanding I ventured into calculus and unsurprisingly failed to grasp its essence ,obviously i wasn't WATCHING CLOSELY. So coming back to our question.To answer that we need to delve into something known as Zeno's Paradox . Consider a race b/w a hare and a tortoise, where tortoise is given a head-start of 1m (Tortoise starts race 1m ahead of hare)also assume that hare can run with twice the speed of tortoise (let's say their speeds are 2 m/s and 1 m/s respectively. Zeno's paradox says, given these conditions, hare can never overtake tortoise despite the fact that former runs faster than the latter...