if Sn = nC0 nC1 + nC1 nC2 + + nCn-1 - Maths - Binomial Theorem

Question

if Sn = nC0
nC1 + nC1
nC2 + + nCn-1
nCn and if Sn+1/Sn =
15/4 then n is equal to

Rahul Raj · Accepted Answer

Dear student

(1+x)n=C0n+C1nx+ +Cnnxn(1+1/x)n=C0n+C1n(1/x)+
+Cnn1/xnSn= coefficient of x in (1+x)n(1+1/x)n=coefficient of x in (1+x)2nxn=coefficient of xn+1 in (1+x)2n =Cn+12nSn+1=C(n+1)+12(n+1)=Cn+22n+2Sn+1Sn=154Cn+12nCn+22n+2=1542n+2! n+2!n!×n+1!n-1!2n!=154(2n+2)(2n+1)(n+2)n=15416n2+24n+8=15n2+30nn2-6n+8=0n=2,4

Regards

if Sn = nC0. nC1 + nC1.nC2 + ..... + nCn-1 . nCn and if Sn+1/Sn = 15/4 then n is equal to

if S_n = ⁿC₀. ⁿC₁ + ⁿC₁.ⁿC₂ + ..... + ⁿC_n-1 . ⁿC_n and if S_n+1/S_n = 15/4 then n is equal to