Question (Section 3.2, Question 4)

Equation 3.1 is:

Answer

Pascal <- matrix(,nrow=11, ncol=11)
for (n in 0:10){
  for (j in 0:n){
    Pascal[n+1,j+1] <- choose(n-1,j) + choose(n-1,j-1)
  }
}

print(Pascal, na.print = " ", quote = FALSE)

##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
##  [1,]    1                                                    
##  [2,]    1    1                                               
##  [3,]    1    2    1                                          
##  [4,]    1    3    3    1                                     
##  [5,]    1    4    6    4    1                                
##  [6,]    1    5   10   10    5    1                           
##  [7,]    1    6   15   20   15    6    1                      
##  [8,]    1    7   21   35   35   21    7    1                 
##  [9,]    1    8   28   56   70   56   28    8    1            
## [10,]    1    9   36   84  126  126   84   36    9     1      
## [11,]    1   10   45  120  210  252  210  120   45    10     1