Skip to main content
Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblema 47
Capitolo 9, Problema 47

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

Guida verificata passo dopo passo
1
Identify the pattern in the sum: the terms are consecutive integers starting from 1 up to 30.
Recognize that the sum can be expressed as the sum of \( i \) where \( i \) takes on integer values from 1 to 30.
Write the summation notation using the sigma symbol \( \sum \), the index of summation \( i \), the lower limit 1, and the upper limit 30.
Express the sum as \( \sum_{i=1}^{30} i \), which means adding all integers \( i \) starting at 1 and ending at 30.
This notation compactly represents the original sum \( 1 + 2 + 3 + \cdots + 30 \) in a concise mathematical form.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Summation Notation

Summation notation is a concise way to represent the sum of a sequence of terms using the Greek letter sigma (∑). It includes an index of summation, lower and upper limits, and the general term to be summed. For example, ∑ from i=1 to n of a_i represents adding terms a_1 through a_n.
Video consigliato:
05:18
Interval Notation

Index of Summation

The index of summation is a variable, often i, that represents the position of each term in the sum. It starts at the lower limit and increments by one until it reaches the upper limit. This index helps define each term in the sequence being summed.
Video consigliato:
03:50
Adding & Subtracting Like Radicals

Arithmetic Series

An arithmetic series is the sum of terms in an arithmetic sequence, where each term increases by a constant difference. For example, 1 + 2 + 3 + ... + 30 is an arithmetic series with a common difference of 1. Recognizing this helps in expressing the sum using summation notation.
Video consigliato:
5:17
Arithmetic Sequences - General Formula
Pratica correlata
Domanda del libro di testo

Express each repeating decimal as a fraction in lowest terms. 0.5‾=510+5100+51000+510,000+⋯0.\(\overline{5}\)=\(\frac{5}{10}\)+\(\frac{5}{100}\)+\(\frac{5}{1000}\)+\(\frac{5}{10,000}\)+\(\cdots\)

994
views
Domanda del libro di testo

Express each repeating decimal as a fraction in lowest terms. 0.47‾=47100+4710,000+471,000,000+⋯0.\(\overline{47}\)=\(\frac{47}{100}\)+\(\frac{47}{10,000}\)+\(\frac{47}{1,000,000}\)+\(\cdots\)

987
views
Domanda del libro di testo

Find the term indicated in each expansion. (x2 + y)22; the term containing y14

45
views
Domanda del libro di testo

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

∑i=130(−3i+5)\(\sum\)_{i=1}^{30} (-3i + 5)

900
views
Domanda del libro di testo

Express each sum using summation notation. Use 11 as the lower limit of summation and ii for the index of summation. 2+22+23+⋯+2112+2^2+2^3+\(\cdots\)+2^{11}

1031
views
Domanda del libro di testo

Find the sum of each infinite geometric series. 2 - 1 + 1/2 - 1/4 + ...

1318
views
1
rank