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Construct a Pascal's triangle to write a binomial expansion for a given positive integral exponent.

Construct a Pascal's triangle to write a binomial expansion for a given positive integral exponent.

Grade:11

1 Answers

Mayank Ranka
askIITians Faculty 277 Points
2 years ago
Hi,
Here’s your solution to construct a Pascal’s triangle so that you can write a binomial expansion
Suppose your positive integral exponent is(a + b)n, where a + b is any binomial and n is a whole number. Look for patterns.
707-1180_Screenshot 2021-12-29 201033.png

For any binomial a + b and any natural number n,
(a + b)n= c0anb0+ c1an-1b1+ c2an-2b2+ .... + cn-1a1bn-1+ cna0bn,
where the numbers c0, c1, c2,...., cn-1, cnare from the (n + 1)-st row of Pascal’s triangle.


Thanks
Regards
Ankit Gupta

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