8.4k views
0 votes
Find the 20th term in the expansion of (a + b)^22

User Meeque
by
8.4k points

1 Answer

2 votes

Answer:

The 20th term in the expansion of (a + b)^22 can be found using the binomial theorem. The general term in the expansion of (a + b)^n is given by:

T_r = (n choose r) a^(n-r) b^r

where (n choose r) is the binomial coefficient, which is equal to n! / (r! (n-r)!).

Therefore, the 20th term in the expansion of (a + b)^22 is:

T_20 = (22 choose 20) a^(22-20) b^20

= (22 choose 20) a^2 b^20

Using the formula for the binomial coefficient, we have:

(22 choose 20) = 22! / (20! 2!) = (22*21) / 2 = 231

Substituting this value into the expression for T_20, we get:

T_20 = 231 a^2 b^20

Therefore, the 20th term in the expansion of (a + b)^22 is 231 a^2 b^20.

User Hamy
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories