Question:
If the number of terms in (x+1+1/x)^n (n E N), is 301,then n is greater than (a)152 (b)151 (c)150 (d) 149
Answer:
The number of terms in the (a + b + c)n = {(n + 2)*(n + 1)}/2
Given, number of terms in the (x + 1 + 1/x)n = 301
=> {(n + 2)*(n + 1)}/2 = 301
=> (n + 2)*(n + 1) = 301 * 2
=> n2 + 3n + 2 = 602
=> n2 + 3n + 2 - 602 = 0
=> n2 + 3n - 600 = 0
=> n2 + 3n - 600 = 0
Now, from the option all values of n satisfy this equation.
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