Use Mathematical Induction to Prove the Given Statement for All $$\sum _ { i = 1 } ^ { n } 2 i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 3 }$$

question 187

Short Answer

Use mathematical induction to prove the given statement for all positive integers n.
- $$\sum _ { i = 1 } ^ { n } 2 i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 3 }$$

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Definitions:

Critical Value

A point on the scale of the test statistic beyond which we reject the null hypothesis; it defines the cutoff point for significance.

Significance Level

A threshold in hypothesis testing that determines the probability of rejecting a true null hypothesis, commonly represented by α.

Degrees of Freedom

A concept in statistics that represents the number of independent values or quantities which can be assigned to a statistical distribution.

Categories

Distinct groups or classes into which data or items can be classified.