PROBLEM 10E

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]

= [n]

=

= nCr

Hence the proof.