Binomial TheoremHard
Question
In the expansion of 
, n ∈ N, if the sum of the coefficients of x5 and x10 is 0, then n is :
, n ∈ N, if the sum of the coefficients of x5 and x10 is 0, then n is :Options
A.25
B.20
C.15
D.None of these
Solution
General term =
(-1)n-r x5r-2n If 5r - 2n = 5, then 5r = 2n + 5 ⇒ r =
+ 1If 5r - 2n = 10, then 5r = 2n + 10 ⇒ r =
+ 2Let n = 5k
Now
⇒
= 0⇒ k = 3 ⇒ n = 15
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