ADDITION OF FIRST “N” NATURAL NUMBERS
Dr. Sonjai Kumar, PhD, CFIRM Certified Risk Management Professional, IRM
PhD in Risk Management
I got a call from my father and, he asked me to write the following:
How to add first n natural number without using the formula, Let we have to add 1to 10
1+2+3+4+5+6+7+8+9+10 Call this series as (1), we have to add the total of this series
Write another series in the reverse order as
10+9+8+7+6+5+4+3+2+1 Call this series as (2)
Add the two series by column, we get
11+11+11+11+11+11+11+11+11+11
This is equal to
11 times 10
That is, 11*10 call this (3)
(3), is a sum of two series of first 10 natural number,
Therefore, the sum of series (1) is half of (3) = 11*10/2
Like this sum of series of any numbers, cal be calculated, like sum of 1 to 5000 = 5001*5000/2
The formula for sum of first n natural numbers are n*(n+1)/2
If n = 10, we get 10*11/2 same as above.
Why I am sharing this with you because this is truly inspiring as these methods are developed by my father who lost his both eyes in Glaucoma and cannot see anything. He is using his brain to keep himself busy and come out with such fantastic solutions. His brain never rests and working on something or other. He is masters in Statistics (1962)
A true inspiration for those who think that life is misery with healthy mind and body.
Actuarial Team Lead at Accenture
8 年Great Its truly inspiring
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8 年Dear Mr.Sonjai...Thanks for sharing this. Learning is "Need to condition the mind to receive, store and process knowledge/information" as was practiced then, during your father's times. Now we are taught to condition the mind for computing the CTC of propspective employer and hence we need a calculator to compute 12*5. Your father may have lost his external sight, but he has the inner sight given by the Lord,glowing and going strong. I am reminded of the parable in Mathew 25 of Holy Bible, which John Milton alludes in one of his sonnets "On his blindness".