Αποτελέσματα Αναζήτησης
6 ημέρες πριν · a) Find a formula for 1/1·2 + 1/2·3 + · · · + 1/n(n+1) by examining the values of this expression for small values of n. b) Prove the formula you conjectured in part (a).
4 ημέρες πριν · According to the problem, we have given that 1 + 2 + 3 +...... + n = 45 and we need to find the value of 13 + 23 + 33 +...... + n3. Let us consider 1 + 2 + 3 +...... + n = 45 --- (1). We know that sum of first n-natural numbers is n(n + 1) 2. We use this result in equation (1). ⇒ n(n + 1) 2 = 45.
6 ημέρες πριν · Use a proof by contraposition to show that if x + y ≥ 2, where x and y are real numbers, then x ≥ 1 or y ≥ 1. discrete math Prove the proposition P(1), where P(n) is the proposition “If n is a positive integer, then n² ≥ n.”
4 ημέρες πριν · define factorial(n): f := 1 for i := 1, 2, 3, ..., n: f := f * i return f. or using recursion based on its recurrence relation as define factorial(n): if (n = 0) return 1 return n * factorial(n − 1) Other methods suitable for its computation include memoization, dynamic programming, and functional programming.
2 ημέρες πριν · A partition of a positive integer n n is an expression of n n as the sum of one or more positive integers (or parts ). The order of the integers in the sum "does not matter": that is, two expressions that contain the same integers in a different order are considered to be the same partition.
4 ημέρες πριν · In combinatorics, a permutation is an ordering of a list of objects. For example, arranging four people in a line is equivalent to finding permutations of four objects. More abstractly, each of the following is a permutation of the letters a, b, c, a,b,c, and d: d:
5 ημέρες πριν · Let an inverse demand function for a commodity be $𝑝 = e^{\frac{-x}{2}$, where 𝑥 is the quantity and 𝑝 is the price. Then, at 𝑝 = 0.5, the consumer surplus is equal to _______ (rounded off to two decimal places).
