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The product of four consective integers is one less than a perfect square?
Suppose the smallest of the integers is n. Then the product of the four consecutive integers is n*(n+1)*(n+2)*(n+3) =(n2+3n)(n2+3n+2) = n4+6n3+11n2+6n So product +1 = n4+6n3+11n2+6n+1 which can be factorised as follows: n4+3n3+n2 +3n3+9n2+3n + n2+3n+1 =[n2+3n+1]2 Thus, one more that the product of four consecutive integers is a perfect square.
What happens if 1 is added to the product of any four consecutive integers and why does it happen?
The result appears to be the square of an integer, but I don't know why. n(n+1)(n+2)(n+3) n4+6n3+11n2+6n. If n 1 then the sum is 24 and adding 1 yields 25 or 52. If n 2. them the sum is 120 and adding 1 yields 121 or 112. If n 5 the sum is 1680 and adding 1 yields 1681 or 412.
What is next in the sequence 7 8 10 14 22?
It could be 37. Use Un = (n4 - 6n3 + 18n2 - 18n + 168)/24 with n = 6
What number comes next 1 4 9 18 35?
Given any number it is possible to find a polynomial of order 5 such that it is a position-to-term rule for the above five and the additional number. The simplest polynomial of order 4 gives Un = (n4 - 6n3 + 23n2 - 6n)/12 for n = 1, 2, 3, ... and accordingly, the next number is 66.
What is the next number in sequence 2 9 20 37 64 107?
Given any number it is easy to find a polynomial rule of order 6 such that the first six numbers are the above six and the seventh is the given number. That is, I can find a rule so that anynumber can be the "next" in the sequence.In this case, you can fit the following quartic:Un = (n4 - 6n3 + 35n2 + 6n - 12)/12 for n = 1, 2, 3, ...and accordingly, the next number is 174.
What is 12-n4?
12-n4 = 8
What is the next number in the series 3 4 6 7 9?
33. The sequence (not series) can be defined by Un = (n4 - 6n3 - 4n2 + 63n - 36)/6 for n = 1, 2, 3, ...
What is n over 18 x 6 over n to the 4th power?
(n/(18*6))/n4=(n/108)/n4 ;Multiply 18 and 6(n/108)*(1/n4) ;Multiply by the reciprocal of n4, which is just 1 over n4n/(n4*108) ;The n4 will go in the bottom of the fraction1/(108n3) ;n over n4 will give you 1 over n3
What are the first five terms of the sequence whose nth term is N4 plus 225?
2,1,0 is th sequence of its terms
P2nr sin180n and p32 n4 find r?
P2nr sin180n and p32 n4 find r
What county does london n4 come under?
N4 isn't from a county. It is the code for the North London suburb of Haringay.
What is C N4 H12?
there is no such compound
