MathsGee Answers is Zero-Rated (You do not need data to access) on: Telkom | Dimension Data | Rain | MWEB
First time here? Checkout the FAQs!
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
Show that $s_{n} \leq 2$ for all $n .$ (Hint: Use induction)
in Mathematics by Bronze Status (8,688 points) | 15 views

1 Answer

0 like 0 dislike
Best answer

The case for $n=1$ is easily true as $s_{1}=\sqrt{2} \leq 2$. Assuming the contention hold for $n=k-1$, then
s_{k}=\sqrt{2+\sqrt{s_{k-1}}} \leq \sqrt{2+2}=2
where the inequality above follows from the induction hypothesis.
by Bronze Status (8,688 points)

Related questions

MathsGee provides answers to subject-specific educational questions for improved outcomes.

On MathsGee Answers, you can:

1. Ask questions
2. Answer questions
3. Comment on Answers
4. Vote on Questions and Answers
5. Donate to your favourite users

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

ZeroEd Search Engine

Other Tools

MathsGee ZOOM | eBook