What exactly does "solve" mean? Are you supposed to find the sum of this series, or do you only need to say that it converges or diverges?Hockeystar said:Homework Statement
Solve 1 + 1/8 + 1/27 + 1/64...
Homework Equations
Stuck here.
The Attempt at a Solution
I know the series is infinitetly adding 1/n^3. I know it should converge. How do I solve as lim x--> infinity. Teacher never gave us any info, he just said use number sense.
A converging sequence is a sequence of numbers that approaches a specific limit as the number of terms in the sequence increases. In other words, the terms in the sequence get closer and closer to a certain value as the sequence goes on.
To solve a converging sequence, you can use the formula for the sum of an infinite geometric series, which is Sn = a / (1-r), where a is the first term and r is the common ratio. Alternatively, you can find the limit of the sequence by taking the limit as n approaches infinity of the nth term in the sequence.
The common ratio in this sequence is 1/8. This means that each term in the sequence is multiplied by 1/8 to get the next term.
The limit of this sequence is 1. As the number of terms in the sequence approaches infinity, the terms get closer and closer to 1, but never quite reach it.
Converging sequences can be used in various real-life applications, such as in finance and economics to calculate compound interest or in physics to model exponential decay. They can also be used in computer algorithms and data analysis to estimate and predict future values based on past trends.