Sum of consecutive numbers - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
$100$ consecutive natural numbers with no primes Additionally, Is it possible to have $1000$ consecutive natural numbers with exactly $12$ primes between them? I have an intuition that we have to form a recurrsive relation and solve it But I am stuck
Find the three consecutive numbers - Mathematics Stack Exchange Any consecutive three numbers can be the answers as the multiplication of the first and third numbers would be 1 less than the square of the number in the middle $$(n-1)(n+1) = n^2 - 1$$ For example, 1, 2, 3 ==> 1*3 = 3 is 1 less than 2*2 = 4
Why are the differences between consecutive squares equal to the . . . The easiest way to I think about the difference between consecutive powers ( squared cubed or whatever) is using binomial theorem For example : $(n+1)^4 - n^4 = n^4 + 4n^3 + 6n^2 + 4n + 1 - n^4 = 4n^3 + 6n^2 + 4n + 1$, with the binomial coefficients found by Whatever method you prefer
Sum of Consecutive Integers - Mathematics Stack Exchange The meaning of the questions: given n, n can be written in the form of at least two consecutive positive integers and the number of species Ideas: Let n can be written as a, a +1, a +2 a + k-1's and (a> = 1), i e , n = (a + a + k-1) * k 2 If k is odd, then, N = (A + (k-1) 2) * k If k is even, then (a + a + k-1) is an odd number
probability - What is the expected number of times a dice has to be . . . This argument generalizes to more than $2$ consecutive 6's by induction For example, if you want $3$ consecutive 6's, you consider sequences that look like this: $$ ?????66? $$ The average length of a sequence of this type is $42 + 1 = 43$ Therefore, the answer is $43 \cdot 6 = 258$ It's not hard to generalize this situation
Probability of two consecutive events happening in a sequence Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Consecutive Odd Numbers? - Mathematics Stack Exchange When doing some exercises on Khan Academy, the following question came up: "The sum of 3 consecutive odd numbers is 69 What is the third number in this sequence?" My answer was 27 because I thought -Odd- Numbers to show up as = 1, 3, 5, 7, etc Apparently, it consists of x, 2, 4, 6, etc
calculus - What is the definition of consecutive roots of a . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers