Question
Let $F$ be the function such that $F(n)$ is the sum of the first $n$ positive integers. Give a recursive definition of $F(n) .$
Step 1
The base case is when $n=1$. According to the problem, $F(n)$ is the sum of the first $n$ positive integers. So, when $n=1$, $F(1)$ is the sum of the first positive integer, which is 1. Therefore, we have: \[F(1)=1\] Show more…
Show all steps
Your feedback will help us improve your experience
Prathan Jarupoonphol and 60 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Give a recursive definition of $S_{m}(n),$ the sum of the integer $m$ and the nonnegative integer $n .$
Induction and Recursion
Recursive Definitions and Structural Induction
Find a function $f(n)$ that identifies the $n$ th term $a_{n}$ of the following recursively defined sequences, as $a_{n}=f(n).$ $$a_{1}=1 \text { and } a_{n+1}=(n+1) a_{n} \text { for } n \geq 1$$
Sequences and Series
Sequences
Find a function $f(n)$ that identifies the $n$ th term $a_{n}$ of the following recursively defined sequences, as $a_{n}=f(n).$ $$a_{1}=2 \text { and } a_{n+1}=(n+1) a_{n} / 2 \text { for } n \geq 1$$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD