# Ex 8.1,14 - Chapter 8 Class 11 Binomial Theorem (Deleted)

Last updated at Jan. 29, 2020 by Teachoo

Expansion

Ex 8.1,1
Deleted for CBSE Board 2022 Exams

Ex 8.1,3 Deleted for CBSE Board 2022 Exams

Ex 8.1, 5 Deleted for CBSE Board 2022 Exams

Ex 8.1,4 Important Deleted for CBSE Board 2022 Exams

Ex 8.1,2 Important Deleted for CBSE Board 2022 Exams

Example 1 Deleted for CBSE Board 2022 Exams

Ex 8.1,11 Deleted for CBSE Board 2022 Exams

Misc 6 Deleted for CBSE Board 2022 Exams

Ex 8.1,12 Important Deleted for CBSE Board 2022 Exams

Misc 5 Important Deleted for CBSE Board 2022 Exams

Ex 8.1,14 Important Deleted for CBSE Board 2022 Exams You are here

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Proving binomial theorem by mathematical induction

Last updated at Jan. 29, 2020 by Teachoo

Ex 8.1, 14 (Method 1) By Binomial Theorem, Putting b = 3 and a = 1 in the above equation Prove that β_(π=0)^πβγ3^π nCrγ β_(π=0)^πβnCr π^(π β π) π^π β_(π=0)^πβnCr 1^(πβπ) 3^π Hence proved Ex 8.1, 14 (Method 2) β 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 β¦ β¦. For r = n, 3^π nCn nC0 30 + nC1 31 + nC2 32 + β¦ β¦β¦β¦ + nCn β 1 3n β 1 + nCn 3n Prove that = nC0 30 + nC1 31 + nC2 32 + β¦β¦β¦β¦β¦β¦ + 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 + β¦β¦ .+ 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 + β¦β¦.+ nCn-1 a1 bn-1 + nCn a0 bn = (1 + 3)n = (4)n = R.H.S Hence proved