Do you know what is a Pascal triangle and what is its use?
Solution :: A Pascal triangle is used to calculate the binomial coefficients without much
struggle. The triangle is drawn as follows.
Start with 1 (This is the first row element,which can be said as 0! )
Now the second row can be obtained by adding the two elements of the first row
(i.e., 1 and 1)
The third row is obtained by writing the end terms as 1 and the remaining by
adding the terms in the previous row and which are present above it.
The subsequent rows can be obtained in the same manner...
1
1 - 1
1 - 2 - 1
1 - 3 - 3 - 1
(1+2) (2+1)
1 - 4 - 6 - 4 - 1
(1+3) (3+3) ( 3+1)
1 - 5 - 10 - 10 - 5 - 1
(1+4) (4+6) (6+4) (4+1)
1 - 6 - 15 - 20 - 15 - 6 - 1
1 - 7 - 21 - 35 - 35 - 21 - 7 - 1
1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1
Solution :: A Pascal triangle is used to calculate the binomial coefficients without much
struggle. The triangle is drawn as follows.
Start with 1 (This is the first row element,which can be said as 0! )
Now the second row can be obtained by adding the two elements of the first row
(i.e., 1 and 1)
The third row is obtained by writing the end terms as 1 and the remaining by
adding the terms in the previous row and which are present above it.
The subsequent rows can be obtained in the same manner...
1
1 - 1
1 - 2 - 1
1 - 3 - 3 - 1
(1+2) (2+1)
1 - 4 - 6 - 4 - 1
(1+3) (3+3) ( 3+1)
1 - 5 - 10 - 10 - 5 - 1
(1+4) (4+6) (6+4) (4+1)
1 - 6 - 15 - 20 - 15 - 6 - 1
1 - 7 - 21 - 35 - 35 - 21 - 7 - 1
1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1
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