Check sibling questions

Example 14 - Find the rth term from end in expansion of (x + a)^n

Example 14 - Chapter 8 Class 11 Binomial Theorem - Part 2
Example 14 - Chapter 8 Class 11 Binomial Theorem - Part 3

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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, First Term = A = n + 1 Common difference = 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 And, 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.