Everybody on this earth wants to do things to please their near and dear ones. The near and dear ones are the one’s whose opinions and thoughts matter.
Sometimes, people do things which they know will make their loved ones feel happy. But they don’t know how much it will make them feel happy. This is one reason when things Happiness is a moment of life, which is not forever. But the feelings that this moment generates will always be there in one’s heart & will be cherished forever. These memories will bring a mite of smile even during the bad phase of life. I still remember a piece of advice from one of my close friends – “Wherever you go, whatever you do. Always have a camera. Always try to capture the things that you like. Of course a camera can never capture the feeling, but all you need to do is to capture the moment. Feelings will always be captured by your heart.”
Gradually, I realized how veracious he was. This is the precise reason I like to click & get clicked.
A few months back, my parents were on a Europe tour to finally meet me in London. It was a tour initiated by me, which commenced in Italy & concluded in London. I knew it will make them feel happy. But, the feeling of happiness was entirely at a different level from what I expected. I could actually make out the sense of happiness, success, satisfaction & above all reaching the final destination - about 6700 kilometres - & see me. The moments were captured & the feelings are resurrected every time I see those moments.
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| euro Tour (april'08) |
Kodak Moments :)J
I read somewhere a formula to calculate the number of powers of 2 in a factorial (100!). I then spent days to identify how this can be proved & generalized. After searching for days, I found a way & an excellent explanation. Here it goes,
Lets assume, we have a number n! for which we want to find the maximum value of k, such that n! is divisible by p^k (here p is a prime number). In simpler terms, the number of powers of p in n!.
The trick is simple:
n/p + n/p^2 + n/p^3.....
This can best be explained by an example:
Lets consider n as 100!, p as 5.Then, K = 100/5 + 100/5^2 + 100/5^3K = 20 + 4 + 0K = 24
Every 5th multiple contributes to 1 value in K, every 25th multiple contributes to 2 values in K (5*5). Out of th2 2 values in 25th multiple, we have already counted 1 value in 5th multiple.
I hope, I'm able to clarify it to some extent.
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