Explanation Given information: The triangular number in terms of a sequence u 1 = 1 ; u n + 1 = u n + ( n + 1 ) . Formula used: The sum of natural numbers from 1 to n + 1 is represented by ( n + 1 ) ( n + 2 ) 2 . Proof: Let u 1 = 1 ; u n + 1 = u n + ( n + 1 ) That is, u n + 1 = u n + ( n + 1 ) = 1 + 2 + 3 + .... + n + ( n + 1 ) = n ( n + 1 ) 2 + ( n + 1 ) By simplifying, u n + 1 = ( n + 1 ) ( n + 2 ) 2 Consider the equilateral triangle. In the triangle, place the objects on the lines, starting with first object on the first line, second object on the second line, third object on the third line and so on until the last object n + 1 on the line n + 1 . Therefore, the triangular number counts objects arranged in an equilateral triangle. The n + 1 th triangular number is the number of objects on the triangular arrangement with n + 1 objects on each sides and The triangular numbers is equal to the sum of the n + 1 natural number from 1 to n + 1 that represented by ( n + 1 ) ( n + 2 ) 2 . Here, u n + 1 = ( n + 1 ) ( n + 2 ) 2 Thus, the terms of a sequence u 1 = 1 ; u n + 1 = u n + ( n + 1 ) called the triangular numbers

Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)

10th Edition

ISBN: 9780321978981

Author: Michael Sullivan

Publisher: PEARSON

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 12.1, Problem 101AYU

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To prove: The numbers 1,3,6,10,15,21,28 are called triangular.

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Chapter 12.1, Problem 100AYU

Chapter 12.1, Problem 102AYU

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Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. 8+x f(x) = x(x-1) (Use a comma to separate answers as needed.) OA. The function f is discontinuous at the single value x = OB. The function f is discontinuous at the single value x = OC. The function f is discontinuous at the two values x = OD. The function f is discontinuous at the two values x = not oo or -0. OE. The function f is discontinuous at the two values x = The limit is The limit does not exist and is not oo or - co. The limits for both values do not exist and are not co or - co. The limit for the smaller value is The limit for the larger value does not exist and is The limit for the smaller value does not exist and is not co or - co. The limit for the larger

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Chapter 12 Solutions

Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)

Ch. 12.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 12.1 - True or False A function is a relation between two...Ch. 12.1 - Prob. 3AYU Ch. 12.1 - True or False The notation a 5 represents the...Ch. 12.1 - True or False If is am integer, then Ch. 12.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 12.1 - The notation a 1 + a 2 + a 3 ++ a n = k=1 n a k...Ch. 12.1 - Prob. 8AYU Ch. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - Prob. 10AYU

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To prove: The numbers 1 , 3 , 6 , 10 , 15 , 21 , 28 are called triangular.

Solution Summary: The author explains that the triangular number is equal to the sum of the n+1 natural number from 1 to

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To prove: The numbers 1,3,6,10,15,21,28 are called triangular.

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Chapter 12 Solutions