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Find the 20th term in the expansion of (a + b)^22

User Meeque
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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
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