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  • Find the value of r, if the coefficients of(2r + 4)th and (r – 2)th terms in the expansion of (1 + x)^18 are equal.

Find the value of r, if the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal.

 

Answers (1)

Given: (1+x)18

Now, T(2r+3)+1 is the (2r + 4)th term

 Thus, T(2r+3)+1 = 18C2r+3 (x)2r+3

Now, T(r-3)+1 is the (r-2)th term

Thus, T(r-3)+1 = 18Cr-3 xr-3

Now, it is given that the terms are equal in expansion,

Thus,

  18C2r+3 = 18Cr-3

i.e., 2r + 3 + r – 3 = 18 …… (nCx = nCy gives x + y = n)

Thus, 3r = 18

Therefore, r = 6

Posted by

infoexpert22

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