Mathematical Induction and Binomial Theorem
What is the sum of all the possible values of x, if the fifth term in the expansion of is 35 and the coefficients of 2nd, 3rd and 4th terms in the expansion are in AP?
i) n! > 3n for some n ∈ N
ii) For any positive integer n, 6n – 1 is divisible by 5
iii) 3n > n2 for any positive integer n greater than 2
iv) The product of three consecutive natural numbers is always divisible by 12
If the sum of the coefficients in the expansion of (1 + 5x)n is 46656, the greatest term in the expansion for is
Among the numbers 55, 78, 135 and 406, which one cannot be the number of terms in the expansion of (x − 2y + 32)n?
If the difference between the coefficients of the terms preceding and succeeding the term that is independent of x in the expansion of is, then what is the value of α?