![]() Continuing to calculate the successors of numbers, we obtain the list of the following seven numbersī) Start with number 96. The successor of the number 164 is number 164+1=165. Its successor is 163+1=164, so the next number in the list is number 164. Here number n-1 is the predecessor of the number n, number n-2 is the predecessor of the number n-1, and so on.ĮXAMPLE: Write seven consecutive integers:Ī) in ascending order starting from number 163 ī) in descending order starting from number 96. On the other hand, if we need consecutive numbers written in descending order, then we start with an arbitrary number n and write after each number its predecessor, Here number n+1 is the successor of the number n, number n+2 is the successor of the number n+1, and so on. If we want to mathematically set consecutive numbers starting with an arbitrary number n, it is also easy to do, just write after each number its successor,Īnd get the list of consecutive numbers written in ascending order. The list of these three numbers looks like If n is a given number, then its predecessor is the number n-1 and its successor is the number n+1. This can be written using a mathematical notation. Predecessor of the number, the number itself and successor of the number are always three consecutive numbers. In the set of integers each number has both, the successor and predecessor. In the set of whole numbers, number 1 has the predecessor but number 0 hasn’t. In the set of natural numbers, number 1 has no predecessor because 1-1=0 is not a natural number. In the sets of natural numbers and whole numbers each number has the successor. So, number 43 is the predecessor of 44 because 44-1=43. If we subtract 1 from any natural number, we get the previous number called the predecessor of the given number. For example, the successor of 26 is 26+1=27. If we add 1 to any natural number, we get the next number called the successor of the given number. What day of the week and what number was six days ago? Sometimes we solve real-life problems involving consecutive natural numbers in reverse order, from largest to smallest.ĮXAMPLE: Today is Friday, 13 th. SOLUTION: If the oldest child was born in 2007, the next child was born in 2008, and all other children – in 2009, 2010, 2011, 2012 years. List all the years of birth of all children. ![]() In practice, we often start counting consecutive numbers from any number.ĮXAMPLE: The years of birth of six children are six consecutive natural numbers, and the oldest child was born in 2007. Natural numbers, whole numbers, integers – all these numbers follow each other continuously in regular ascending order and are consecutive numbers. Numbers that follow each other continuously in regular counting order or pattern are called consecutive numbers. ![]() So, we are ready to define consecutive numbers. Hence, consecutive natural numbers are the numbers that follow each other in order from the smallest to the greatest, increasing by 1. Natural numbers are numbers used in counting, 1, 2, 3, 4, 5, 6, … As we can see the difference between any two neighbor natural numbers is 1. The easiest way to get acquainted with consecutive numbers is to remind natural numbers. Depending on whether the first row has an even number or an odd number of seats, we will get consecutive even or odd natural numbers of seats in this sector. ![]() ![]() For example, in a circus, each next row of a sector has 2 more seats than the previous one. Sometimes objects are numbered consecutively in a certain pattern. Why is this happening? Because the pages are numbered with consecutive natural numbers and it makes your life easier. From consecutive numbers to arithmetic seriesįlipping through the pages of the book, on each page you can see the number of the page and it helps you know what is the number of the next page, how many pages are between 35th and 62th pages or how many pages you have read so far.Where f is a cutoff function with appropriate properties. The nth partial sum of the series is the triangular number ∑ k = 1 n k = n ( n + 1 ) 2, The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The parabola is their smoothed asymptote its y-intercept is −1/12. Divergent series The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯. ![]()
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