Blocky pirates

Pirate Adventures - Take command of a pirate vessel as it navigates treacherous waters, or lead a fearless pirate on a journey through mysterious islands. Help these brave adventurers avoid dangerous traps and discover incredible treasures in this captivating Android game. Become a true pirate by exploring distant islands and enigmatic jungles. Maneuver your ship through deadly reefs, and brave the unknown shores as you make your way through thick jungles and ancient temple ruins. Be on the lookout for traps and obstacles as you strive to reach your ultimate goal. Game Features: - Block-style graphics - A variety of unique characters - Exciting levels to conquer - Simple controls for easy gameplay<|endoftext|><|endoftext|> # 2015 AMC 10B Problems/Problem 1. ## Contents. 1 Problem 2 Solution 3 Video Solution 4 See Also ## Problem What is the value of \[2^{-1}+2^{-2}+2^{-3}+2^{-4}+2^{-5}?\] $\textbf{(A)}\ \frac{1}{2}\qquad\textbf{(B)}\ \frac{3}{8}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}\ \frac{5}{16}\qquad\textbf{(E)}\ \frac{3}{16}$ ## Solution. We can rewrite the expression as \[2^{-1}+2^{-2}+2^{-3}+2^{-4}+2^{-5} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}.\] Combining the fractions, we get \[\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} = \frac{16}{32} + \frac{8}{32} + \frac{4}{32} + \frac{2}{32} + \frac{1}{32} = \frac{31}{32}.\] Therefore, the answer is $\boxed{\textbf{(E)}\ \frac{3}{16}}$. ## Video Solution. https://youtu.be/8pZs21Uq0-g ~savannahsolver <|endoftext|>## Mathematical Forums ## Category: High School Olympiads ## Topic: Inequality ## Views: 338 ## [enter: math-user1, num_posts=697, num_likes_received=372] ## [math-user1, num_likes=1] Let $a,b,c>0$. Prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a