SOLUTION: In the expansion of (2x+1)^n, the coefficient of the x^2 term is 40n , where n is a positive integer. Find the value of n.

Algebra ->  Functions -> SOLUTION: In the expansion of (2x+1)^n, the coefficient of the x^2 term is 40n , where n is a positive integer. Find the value of n.       Log On


   

Question 1181925: In the expansion of (2x+1)^n, the coefficient of the x^2 term is 40n , where n is a positive integer. Find the value of n.
Answer by ikleyn(52781) About Me  (Show Source):
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In the expansion of (2x+1)^n, the coefficient of the x^2 term is 40n ,
where n is a positive integer. Find the value of n.
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The coefficient at x^2 is  2%5E2%2AC%5Bn%5D%5E2 = 4%2A%28n%2A%28n-1%29%2F2%29,


so we have this equation


    4%2A%28n%2A%28n-1%29%2F2%29 = 40n,  or


    %28%28n-1%29%2F2%29 = 10

    n-1 = 20

    n = 21.        ANSWER

Solved.