Using mathematical induction prove whether or not the following statement is true for all positive integers n, or show why it is false.

2+6+10+ +4n-2=2n^2

Base case: For , the left side is 2 and the right is , so the base case holds.

Induction hypothesis: Assume the statement is true for , that is

We want to show that this implies truth for , that

The first terms on the left reduce according to the assumption above, and we can simplify the -th term a bit:

so the statement is true for all .

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.

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.