Math miscellaneousEasy
Question
r and n are positive integers r > 1, n > 2 and coefficient of (r + 2)th term and 3rth term in the expansion of (1+x)2n are equal, then n equal
Options
A.3r
B.3r + 1
C.2r
D.2r + 1
Solution
tr+2 = 2nCr+1 xr+1 ; t3r = 2nC3r-1 x3r-1
Given 2nCr+1 = 2nC3r+1 = 2nC3r-1 ⇒ 2nC2n-(r + 1) = 2nC3r-1 ⇒ 2n - r - 1 = 3r - 1 ⇒ 2n = 4r
Given 2nCr+1 = 2nC3r+1 = 2nC3r-1 ⇒ 2nC2n-(r + 1) = 2nC3r-1 ⇒ 2n - r - 1 = 3r - 1 ⇒ 2n = 4r
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