Arithmetic Series Young Gauss and The Sum of the Natural Numbers Gauss told the story that when he was a boy, the teacher ran out of stuff to teach and asked them, in the remaining time before playtime, to compute the sum of all the numbers from 1 to 20 or similar And this is true for all the similar pairs, of which there are

Write the product and sum of the expressions being represented in the rectangular array. Example 3 For each expression, write each sum as a product of two factors. Emphasize the importance of the distributive property.

Use various equivalent expressions to justify equivalency.

Example 4 A new miniature golf and arcade opened up in town. For convenient ordering, a play package is available to purchase. It includes two rounds of golf and 20 arcade tokens, plus three dollars off.

There is a group of six friends purchasing this package. Let g represent the cost of a round of golf and let t represent the cost of a token. Write two different expressions that represent the total amount this group spent. Explain how each expression describes the situation in a different way.

Using the distributive property, write an equivalent expression for part a. Example 6 Rewrite 5a - a - 3b in standard form. Justify each step applying the rules for subtracting and the distributive property.

Exercise 6 Expand each expression and collect like terms.

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Please submit your feedback or enquiries via our Feedback page.So, the verbal expression the sum of a number and 14 can be represented by the algebraic expression n + 6 less a number t 62/87,21 The word less suggests subtraction.

So, the verbal Write a verbal expression for each algebraic expression. other, they are being multiplied. So, the verbal expression. Find the sum of the unknown factors of the smaller areas.

_ + _ = _ that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. Write an expression using the Distributive Property that can be used to find the.

Using Infinite Calculus to find the Sum of the first n Natural Numbers If we form this expression [] We can write the square of any odd number as: [] We can write an odd number as (2n-1), where n is a natural number.

We note that we can find a q value for each of the numbers, so that 8q+1 is equal to the square of the odd number. PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various the sum of the lengths of its sides.

3 m 10 m 9 m 13 m Pool.

Solutions to Examples: First, write the area of each circle in terms of π. Then use the approximation π≈ and compute the area of each circle to the nearest. Before I show you how to find the sum of arithmetic series, you need to know what an arithmetic series is or how to recognize it.

A series is an expression for the sum of the terms of a sequence. For example, 6 + 9 + 12 + 15 + 18 is a series for it is the expression for the sum . The sum of the natural numbers from 1 to n is therefore half the product of the first term plus the last one multiplied by the number of terms.

General Arithmetic Series A pure arithmetic series is one where the difference between successive terms is a constant.

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Factoring Simple Expressions