Pascal's Triangle

How to get value of 11^5 from Pascal Triangle

Piyush Goel

• 2 min read

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), (a2 + 2ax +x2),(a3 + 3a2x +3ax2 + x3) 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.1

 

If we sum up the rows, we get a GP series i.e. 1, 2, 4, 8, 16, 32, 64,…….

2

Now, it’s a very interesting for all of us to get 115 after 114 as 114 =14641 but for 115, the value becomes 161051 which is absent in Pascal triangle practically.

3

So, I get a solution. Let’s see this,

How to get value of 115 from Pascal Triangle (1 5 10 10 5 1)

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1
  1. Put 5 zeroes before 1.

[5 10 10 5 1]

  1. Put 5 with four zeroes.

[10 10 5 1]

  1. Put 10 with three zeroes.

[10 5 1]

  1. Put 10 with two zeroes.

[5 1]

  1. Put 5 with one zero.

[1]

  1. At last, 1 without zero.

1 6 1 0 5 1

Exact value of 115 from Pascal Triangle

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