Interview with Tony Chan (陳繁昌)...
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Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Christian philosopher. Pascal Triangle is really a great work by Pascal & open many options for scholars in mathematics. Pascal’s triangle is a triangular array of the binomial coefficients. It is based on x, (a + x), (a + x)^{2},(a + x)^{3} & soon…..
Put coefficient of x, (a + x), (a^{2} + 2ax +x^{2}),(a^{3 }+ 3a^{2}x +3ax^{2} + x^{3}) as (1),(1,1),(1,2,1),(1,3,3,1) & soon..
Onwards from here, many scholars worked out to put their own theories, so here is my work on Pascal Triangle.
If we sum up the rows, we get a GP series i.e. 1, 2, 4, 8, 16, 32, 64,…….
Now, it’s a very interesting for all of us to get 11^{5} after 11^{4} as 11^{4 }=14641 but for 11^{5}, the value becomes 161051 which is absent in Pascal triangle practically.
So, I get a solution. Let’s see this,
How to get value of 11^{5} from Pascal Triangle (1 5 10 10 5 1) 

100000 50000 10000 1000 50 1 
[5 10 10 5 1]
[10 10 5 1]
[10 5 1]
[5 1]
[1]

1 6 1 0 5 1 
Exact value of 11^{5} from Pascal Triangle 