How many ways can the number 9 be expressed as the sum of the digits 1 or 2?

How many ways can the number 9 be expressed as the sum of the digits 1 or 2?

This question already has answers here: Closed last year. All the positive numbers can be expressed as a sum of one, two or more consecutive positive integers. For example 9 can be expressed in three such ways, 2+3+4, 4+5 or simply 9.

How do you calculate the sum of numbers?

The formula to calculate the sum of integers is given as, S = n(a + l)/2, where, S is sum of the consecutive integers n is number of integers, a is first term and l is last term.

How do you express a number as a sum of consecutive numbers?

Count ways to express a number as sum of consecutive numbers

1. Examples:
2. Approach: The idea is to represent N as a sequence of length L+1 as: N = a + (a+1) + (a+2) + .. + (a+L) => N = (L+1)*a + (L*(L+1))/2. => a = (N- L*(L+1)/2)/(L+1)
3. Time Complexity: O(N^0.5)

What is sum of numbers?

The sum of two numbers is the answer you get when you add them both together. So the sum of 5 and 4 is 9. There was a time when teachers used the word ‘sum’ to name the following addition number sentence: 9 + 5 = 14.

Can every number be written as a sum of consecutive whole numbers?

We can’t write every number as a sum of consecutive numbers – for example, 2, 4 and 8 can’t be written as sums of consecutive numbers. If you add two consecutive numbers together, the sum is an odd number, e.g.

What is sum of consecutive numbers?

An odd number of consecutive numbers has a whole number as an average. This average is always the middle number. So, that means that the sum of the numbers will be: Sum = average \times number of consecutive numbers.

Are there any ways to get a sum of 1?

There’s no two or more numbers that we can add to get a sum of 1 (excluding 0). Let’s try a higher number. Let’s try 4. 4 has addends: 1+1+1+1, 1+2+1, 1+1+2, 2+1+1, 1+3, 2+2, 3+1. Its total is 7.

How to add up to a sum’s with N?

If n is 1: its addends are o. There’s no two or more numbers that we can add to get a sum of 1 (excluding 0). Let’s try a higher number. Let’s try 4. 4 has addends: 1+1+1+1, 1+2+1, 1+1+2, 2+1+1, 1+3, 2+2, 3+1.

How to express a number as a sum of two natural numbers?

Given an integer N, the task is to find the number of ways to represent this number as a sum of 2 or more consecutive natural numbers. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution.

How to find the number of ways to write n?

7) * Conclusion : there exist a one to one correspondance between the number of ways of writing N = cons (m,n) (which is the number of ways of writing N as sum of consecutive integers, as we have seen) and the number of odd divisors of N. * 8) Finally, the number we are looking for is the number of odd divisors of n.