Concept explainers
To find The partial sum of
The partial sum of ∑ n = 1 500 ( n + 8 ) is 129250 .
Given information:
The given sum is ∑ n = 1 500 ( n + 8 ) .
Definition used:
The nth term of the arithmetic sequence has the form a n = a 1 + ( n − 1 ) d ,where a 1 is the first term of the sequence, and d is the common difference.
The sum of finite arithmetic sequence is given by S n = n ( a 1 + a n ) 2 .
Here n is the number of terms, a 1 is the first term of the sequence, and a n is the last terms of sequence.
Calculation:
It is given that ∑ n = 1 500 ( n + 8 ) .
The above sum can be written as follows,
∑ n = 1 500 ( n + 8 ) = ( 1 + 8 ) + ( 2 + 8 ) + ( 3 + 8 ) + ( 4 + 8 ) + ⋯ ( 500 + 8 ) = 9 + 10 + 11 + 12 + ⋯ + 508
Compute the common difference as follows,
d 1 = a 2 − a 1 = 10 − 9 = 1
d 2 = a 3 − a 2 = 12 − 11 = 1
Therefore, the given sequence is an arithmetic sequence.
Compute the partial sum as follows,
S 500 = 500 ( 9 + 508 ) 2 = 250 ⋅ 517 = 129250
Therefore, the sum of the partial arithmetic sequence is 129250 .
The partial sum of
Given information:
The given sum is
Definition used:
The nth term of the arithmetic sequence has the form
The sum of finite arithmetic sequence is given by
Here n is the number of terms,
Calculation:
It is given that
The above sum can be written as follows,
Compute the common difference as follows,
Therefore, the given sequence is an arithmetic sequence.
Compute the partial sum as follows,
Therefore, the sum of the partial arithmetic sequence is
Answer to Problem 65E
The partial sum of
Explanation of Solution
Given information:
The given sum is
Definition used:
The nth term of the arithmetic sequence has the form
The sum of finite arithmetic sequence is given by
Here n is the number of terms,
Calculation:
It is given that
The above sum can be written as follows,
Compute the common difference as follows,
Therefore, the given sequence is an arithmetic sequence.
Compute the partial sum as follows,
Therefore, the sum of the partial arithmetic sequence is
Chapter 8 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning