Question 9 - General Term of Binomial Theorem - Chapter 7 Class 11 Binomial Theorem
Last updated at April 16, 2024 by Teachoo
General Term of Binomial Theorem
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General Term of Binomial Theorem
Last updated at April 16, 2024 by Teachoo
Question 9 In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal. We know that General term of expansion (a + b)n is Tr+1 = nCr anβr br For (1 + a)m + n, Putting n = m + n , a = 1, b = a Tr+1 = n + mCr (1)n + m β r (a)r = n + mCr (a)r Finding coefficient of am ar = am r = m Putting r = m in (1) Tm + 1 = n + mCm (a)m = ((π + π)!)/π!(π + π β π )! (a)m = ((π + π)!)/(π! (π)!) (a)m Hence, coefficient of am is ((π + π)!)/π!(π)! Finding coefficient of an ar = an r = n Putting r = n in (1) Tn + 1 = n + mCn (a)n = ((π + π)!)/π!(π + π βπ )! (a)n = ((π + π)!)/π!(π)! (a)n Hence, coefficient of an is ((π + π)!)/π!(π)! Hence, Coefficient of am = Coefficient of an Hence proved