Ex 8.2, 8 - Find middle terms of (x/3 + 9y)10 - Binomial - Middle term

  1. Chapter 8 Class 11 Binomial Theorem
  2. Serial order wise

Transcript

Ex 8.2,8 Find the middle terms in the expansions of 3 +9 10 Number of terms n = 10 Since n is even. There will be one middle term Middle term = 2 + 1 = 10 2 + 1 = 5 + 1 = 6th term. Hence we need to find 6th term. i.e. T6 We know that general term of (a + b)n is Tr+1 = nCr (a)n-r . (b)r 6th term = T6 = T5+1 of expansion 3 +9 10 Hence r = 5 & n = 5 , a = 3 & b = 9y T5 + 1 = 10C5 3 10 5 . (9y)5 T6 = 10C5 3 5 . (9)5 . y5 = 10! 5! 10 5 ! . 3 5 . (3)2 5 . y5 = 10! 5!5! . 5 35 . 310 . y5 = 10 9 8 7 6 5! 5 4 3 2 1 5! . x5 . 310 35 . y5 = 10 9 8 7 6 5 4 3 2 1 . x5 . 35 . y5 = 10 9 8 7 6 35 5 4 3 2 1 . x5 . y5 = 61236 x5 y5 Hence middle term of 3 +9 10 is 61236 x5 y5

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