Question
Prove that $H_{2^{n}} \leq 1+n$ whenever $n$ is a nonnegative integer.
Step 1
The Harmonic number $H_n$ is defined as the sum of the reciprocals of the first $n$ positive integers, i.e., $H_n = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n}$. Show more…
Show all steps
Your feedback will help us improve your experience
Willis James and 96 other Algebra 2 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
Prove that $n^{2}+1 \geq 2^{n}$ when $n$ is a positive integer with $1 \leq n \leq 4 .$
The Foundations: Logic and Proofs
Proof Methods and Strategy
Prove that n^2 + 1 >= 2^n when n is a positive integer with 1 <= n <= 4.
Prove that for any positive integer $n$ $$2^{n}=\left(\begin{array}{l}n \\0\end{array}\right)+\left(\begin{array}{l}n \\1\end{array}\right)+\left(\begin{array}{l}n \\2\end{array}\right)+\cdots \#\left(\begin{array}{l}n \\n\end{array}\right)$$ $[\text {Hint: } 2=1+1 .]$
Discrete Algebra
The Binomial Theorem
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD