Powers of 2, i.e.Originally Posted by sonymd23
Since the sum of the rows of a Pascal triangle are,
1. predict the result of Alternately adding and subtracting the squares of the terms in the nth row of Pascal's Triangle.
2. given the last four terms of a row of Pascal's Triangle are : 816 , 153 , 18 , 1. determine the last four terms of the next row
3. the number 23040 can be factored into prime divisors as 2x2x2x3x3x5x8x8. determine the number of even divisors of 23040
^ thats the question....can any one solve it....thnx......show ur steps and remember explain...... thnx very much
Its prime factorization is,Originally Posted by sonymd23
Note any divisor must be a form of,
Where,
But since we want is even we need that
Thus, in total we have 9 possibilities for 3 possibilities for and 2 possibilities for
Thus, by the fundamental counting princple in total,
Great mystery of the day - which question are you refering to?Originally Posted by ThePerfectHacker
(Rhetorical question, I know but a casual reader may get lost)
Its zero only when k is even surly?
RonLCode:1 +1 -4 +1 !=0 +1 -9 +9 -1 =0 +1 -16 +36 -16 +1 !=0 and so on
Hello, sonymd23!
#3 has an incorrect phrase in it . . . Is there a typo?
. . And it is easier if you know a particular theorem.
3. The number can be factored into prime divisors as:
. . . . . . but these are not prime divisors
Determine the number of even divisors of .
Theorem
If the prime factorization of is:
. . then the number of divisors of is:
. . (Add one to each exponent, and multiply.)
This includes the divisors and itself.
We have: .
Hence, has: divisors.
How many of these are odd divisors?
. . An odd divisor must be a product of odd factors.
Odd divisors would come from:
. . which has divisors.
Therefore, has: even divisors
. . which verifies TPHacker's solution.