What is?

My friend challenges me to solve the following:

$\color{green}{\quad\text{What would be the solution to:}}$

$\color{#20A900}{\quad\Large\frac{1}{3} + \frac{1}{7} + \frac{1}{8} + \frac{1}{15} + \frac{1}{24} + \frac{1}{26} + \frac{1}{31} + \frac{1}{35} + \cdots}$

#Algebra

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

How are the denominators progressing? I mean what is the pattern?

Yatin Khanna - 4 years, 9 months ago

Not very sure but I couldn't help but notice this: 3=(2^2)-1,7=(2^3)-1,15=(2^4)-1,31=(2^5)-1..... 8=(3^2)-1,26=(3^3)-1...... 15=(4^2)-1(already included) 24=(5^2)-1........ 35=(6^2)-1........

A Former Brilliant Member - 4 years, 9 months ago

My friend simply send me this, and asks me to solve it. At the moment, I can't really tell what the pattern is. I guess it is part of the problem.

Bloons Qoth - 4 years, 9 months ago

Cool! I will definitely try this one..

Yatin Khanna - 4 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$