please help me solve this: a. every whole number greater thsn 4 and less than 20 is the sum of two or more consecutive whole numbers.
a. every whole number greater thsn 4 and less than
20 is the sum of two or more consecutive whole
numbers.
The correct answer is that it is false because 8 cannot
be written that way.
8 can't be the sum of two consecutive integers because
1+2=3, 2+3=5, 3+4=7, 4+5=9, every other pair of consecutive
integers will exceed 8
8 can't be the sum of three consecutive integers because
1+2+3=6, 2+3+4=9, every other group of 3 consecutive ingers
will exceed 8
8 can't be the sum of four consecutive integers because
1+2+3+4=10, and every other group of 4 consecutive ingers
will exceed 8
And of course there is no use to try 5 or more consecutive
integers because even the smallest group of 4 have sum
greater than 8.
Therefore it is false because not every whole number greater
than 4 and less than 20 is the sum of two or more consecutive
numbers. 8 is a counter-example.
b. every whole number between 25 and 50 is the product of two whole numbers greater than 1.
That is false because 29 is a prime number between
25 and 50 and 29 can only be written as a product
of two whole numbers, 29x1.
Edwin
