Can every natural number be expressed as the sum of consecutive natural numbers?

No, not all natural numbers can be expressed this way; for example, powers of 2 cannot.

Which numbers can be expressed as sums of consecutive natural numbers in multiple ways?

Numbers like 15 can be expressed as sums of consecutive numbers in multiple ways, such as 7 + 8 and 4 + 5 + 6.

Fill in the blank: All even numbers can be expressed as a sum of consecutive numbers, except for ___ and ___.

2 and any even number that is a power of 2

True or False: The number zero can be expressed as a sum of consecutive natural numbers.

True, it can be expressed as -1 + 0 + 1.

What is the general form for expressing any four consecutive numbers with plus and minus signs?

The eight expressions can be represented as n + (n+1) + (n+2) + (n+3), n + (n+1) + (n+2) - (n+3), and so on.

True or False: The expression 3g + 5h will always produce an even number.

False, it can produce either an even or odd number depending on the values of g and h.

Demonstrate how to determine if the expression 4m + 2n is always even.

Both 4m and 2n are even for any integer values of m and n, thus their sum is always even.

Fill in the blank: The least common multiple of 9 and 4 is ___.

36

Explain the divisibility rule for 6.

A number is divisible by 6 if it is divisible by both 2 and 3.

Fill in the blank: A number is divisible by 5 if its last digit is ___ or ___.

0 or 5

What is the digital root of the number 489710?

The digital root is 2, obtained by repeatedly summing the digits until a single digit is left.

How can you express a number that gives a remainder of 3 when divided by 5?

It can be expressed in the form 5k + 3, where k is a whole number.