# Example 14 - Chapter 8 Class 11 Binomial Theorem

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Example 14 Find the rth term from the end in the expansion of (x + a)n. We know that (a + b)n = nCo anbo + nC1 an–1b1 +……..+ nCn–1 (a)(n–1) .bn–1 + nCn a0 bn = an + nC1 an–1b1 + ………………………+ nC1 a1bn–1 + bn = bn + nC1 a1 bn–1 +…………………+ nC1 an–1 b1 + an rth term from end = rth term of A.P n + 1, n , n – 1 ……… from starting We know that nth term of A.P = A + (n – 1)D Here A = n + 1 D = n – (n + 1) = n – n – 1 = – 1 rth term from end = A + (r – 1)D = (n + 1) + (r – 1) (–1) = (n – r + 2)th term from stating We know that General term of expansion (a + b)n Tr + 1 = nCr (a)n-r.br Putting r = (n – r + 2) – 1 = n – r +1 a = x & b = a T(n–r+1) + 1 = nCn – r + 1 .(x)n – [n – r + 1] . an – r + 1 = nCn – r + 1 .(x)n- n – r + 1 . an – r + 1 = nCn – r + 1 . xr – 1 . an – r + 1 Hence rth term from end is nCn–r+1 xr – 1 an – r + 1

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.