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Ex 8.2
Ex 8.2, 2 Important Deleted for CBSE Board 2023 Exams
Ex 8.2, 3 Deleted for CBSE Board 2023 Exams
Ex 8.2, 4 Important Deleted for CBSE Board 2023 Exams
Ex 8.2,5 Deleted for CBSE Board 2023 Exams
Ex 8.2 6 Important Deleted for CBSE Board 2023 Exams
Ex 8.2,7 Deleted for CBSE Board 2023 Exams
Ex 8.2,8 Important Deleted for CBSE Board 2023 Exams
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Ex 8.2,10 Important Deleted for CBSE Board 2023 Exams
Ex 8.2,11 Important Deleted for CBSE Board 2023 Exams
Ex 8.2,12 Deleted for CBSE Board 2023 Exams
Last updated at March 16, 2023 by Teachoo
Ex 8.2, 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 an–r br For (1 + a)m + n, Putting n = m + n , a = 1, b = a Tr+1 = n + mCr (1)n + m – 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 = ((𝑛 + 𝑚)!)/𝑚!(𝑛 + 𝑚 − 𝑚 )! (a)m = ((𝑛 + 𝑚)!)/(𝑚! (𝑛)!) (a)m Hence, coefficient of am is ((𝒏 + 𝒎)!)/𝒎!(𝒏)! Finding coefficient of an ar = an r = n Putting r = n in (1) Tn + 1 = n + mCn (a)n = ((𝑛 + 𝑚)!)/𝑛!(𝑛 + 𝑚 −𝑛 )! (a)n = ((𝑛 + 𝑚)!)/𝑛!(𝑚)! (a)n Hence, coefficient of an is ((𝒏 + 𝒎)!)/𝒏!(𝒎)! Hence, Coefficient of am = Coefficient of an Hence proved