The sum of the first n positive integers can be found using the formula n(n+1)/2. how many integers must be added to get 253 as the sum.

22

Step-by-step explanation:

Using the given expression and the sum, we can set up an equation and solve for the value of 'n':

Multiply both sides by '2':  

n(n+1) = 506

Distribute: n² + n - 506 = 0

Factor:  (n + 23) (n - 22) = 0

Set each equation equal to '0' and solve:

n + 23 = 0    n - 22 = 0

n = -23   or n = 22

Since the problem says the integers are positive, then n = 22.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

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