Pascal’s triangle gives amethod for calculating the binomial coefficients; it begins as follows:
The nth row of this triangle gives the coefficients for (a + b)n−1. To find an entry in the table other than a 1 on the boundary, add the two nearest numbers in the row directly above. The equation
called Pascal’s equation, explains why Pascal’s triangle works. Prove that this equation is correct.
Step 1 of 3:
We have to prove the pascal's equation
nCr = n-1Cr + n-1Cr-1
\And how the pascal's triangle works to find the binomial coefficients.
Step 2 of 3 :
We have to prove that
. nCr = n-1Cr + n-1Cr-1
Consider the RHS
n-1Cr + n-1Cr-1 = +
= [ (n-r)+r]
Hence the proof.