A series

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Hi friends!!! As I promised youlast time, here’s the stuff about series.(Not so funnythis time). I don’t know the name of this series (if at all there) and ifsomebody else also studied it before me. But, this series is the most importantthing I felt in understanding Galilean relativity. Be ready with youcalculators…

Suppose I am the king of this worldand you are my chief minister. Now, I order you to find out “the luckiest”person on this earth apart from me, the king of the world himself. How you willproceed? Simple! Well, take a coin and toss it between pair of persons. If world’stotal population is 7 billion then in the first round you will get 3.5 billionwinners. Let us play a second round and 1.75 billion winners will be left.After thirty-three such rounds you will get the person who has won coin tosssuccessively 33 times and no competitor left. He will be the luckiest person onthe earth. Winning toss for 33 consecutive times is not a joke. He deserves theluckiest owner.

Let me explain you mathematicalaspects of this game. We had 7 billion persons and we wanted to find one. So wedivided population in half, then quarter, then (1/8)th and so on. So what we got ultimately was thewinner, the one. Do you know how it works? Put 2, (P = 2) in following formulaand see the results…you will get one. (The luckiest person)

Here is the series

1/P + 1/P² + 1/P³+ 1/P⁴ + …….. ∞ = 1/(P-1) ------------------ <1>

Similar to infinite series, youcan have finite series also. Let us assume our series is limited up to power“V”.

1/P⁰ +1/P + 1/P²+ ……..+ 1/P^v= P^v+1-1 / P^v(P-1) -------------<2>

(How I derived it from equation<1>? You tell me in your comments or ask me for it!!!)

Let us play with this series a littlemore. Let us start from power “v” and end at power “x”.

1/P^v + 1/P^v+1 +1/P^v+2 + ……..+1/P^x = P^x-P^v / P^x+v(P-1)--------<3>

It’s fine!!! You might feel… buthow is it going to help me? Where do I find this series in my life? Well!!! Youhave seen it several times. This is the series which holds secret of Galileanrelativity. Hadn’t this series been there, the whole universe would have been amess. Don’t follow me? Well you are not supposed to be until I show you how itis related to inertia and linear motion. Wait till my next post. Bye bye!!!!

(Don’t mail me this time. Now youcan put your comments on the blog. Write there!!!!)