Puzzler Quik

Can you find the sum of the first 100 perfect squares?

Puzzled?

Here is a hint to help you get going in the right direction:

Don’t actually add up the numbers!

Hint 2:

Find/search up the formula!

Puzzler Think

What is the sum of this infinite geometric series? $$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+…$$

Puzzled?

Here is a hint to help you get going in the right direction:

Do you know how to find the sum of an infinite Geometric Series?

Hint 2:

This series converges towards something(can you find that something?)

ANSWERS TO LAST WEEK’S PUZZLERS

Last Week's Puzzler Quik

Krishay from California was the winner of this shout-out.

When we flip all 100 coins, we expect half of them (50 coins) to be heads, which we put aside. When we flip a second time, we again expect half of them (25 coins out of 50 remaining) to be heads and put aside. When we flip a third time, we again expect half of them (12.5 coins out of 25 remaining) to be heads and put aside. So, the expected total number of coins put aside is 50+25+12.5 = 87.5.

Last Week's Puzzler Think

This week’s shout out goes to Zack from Wyoming! Kudos to him!

Let $y = \sqrt[4]{x}$ , so the equation becomes
$$\begin{align*}
y &= \frac{12}{7 – y} \\
\Rightarrow\quad y^2 – 7y + 12 &= 0 \\
\Rightarrow\quad(y – 3)(y – 4) &= 0,
\end{align*}$$
implying that $y = 3$ or $y = 4$ . Since these are both positive we must have $x = 81$ or $x = 256$ , so the answer is $81 + 256 = \framebox{337}$ .