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

Transcript

Ex 8.1, 14 (Method 1) By Binomial Theorem, Putting b = 3 and a = 1 in the above equation Prove that โˆ‘_(๐‘Ÿ=0)^๐‘›โ–’ใ€–3^๐‘Ÿ nCrใ€— โˆ‘_(๐‘Ÿ=0)^๐‘›โ–’nCr ๐‘Ž^(๐‘› โˆ’ ๐‘Ÿ) ๐‘^๐‘Ÿ โˆ‘_(๐‘Ÿ=0)^๐‘›โ–’nCr 1^(๐‘›โˆ’๐‘Ÿ) 3^๐‘Ÿ Hence proved Ex 8.1, 14 (Method 2) โ€“ Introduction For r = 0, 3^0 nC0 For r = 1, 3^1 nC1 For r = 2, 3^2 nC2 For r = 3, 3^3 nC3 โ€ฆ โ€ฆ. For r = n, 3^๐‘› nCn nC0 30 + nC1 31 + nC2 32 + โ€ฆ โ€ฆโ€ฆโ€ฆ + nCn โˆ’ 1 3n โˆ’ 1 + nCn 3n Prove that = nC0 30 + nC1 31 + nC2 32 + โ€ฆโ€ฆโ€ฆโ€ฆโ€ฆโ€ฆ + nCn-1 3n-1 + nCn 3n Ex 8.1, 14(Method 2) Solving L.H.S This is similar to nC0 an b0 + nC1 an-1 b1 + nC2 an-2 b2 + โ€ฆโ€ฆ .+ nCn-1 a1 bn-1 + nCn a0 bn Where a = 1 , b = 3 And we know that (a + b)n = nC0 an b0 + nC1 an-1 b1 + โ€ฆโ€ฆ.+ nCn-1 a1 bn-1 + nCn a0 bn = (1 + 3)n = (4)n = R.H.S Hence proved

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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.