The probability of an unbiased coin landing on heads or tails is 50/50. What are the chances of flipping the coin 2 times and having them both land on heads. Calculate the probability of flipping the coin 100 times and it landing on heads 100 times in a row. Calculate the probability of it landing nth times in a row with nth flips.

Despite each individual flip having a 50/50 chance to land on heads or tails, explain why as the number of flips increase, the probability of flips landing on heads consecutively drops dramatically

I obviously understand that the coin has a 50% chance to land on heads. For the next flip it also has 50% chance to land on heads but to work this out, do I take the percentage chance and divide it by the number of flips?

$\displaystyle \frac{0.5}{2}\rightarrow \frac{0.25}{3}\rightarrow \frac{0.08333}{4}\rightarrow \frac{0.0208325}{5}=?$

not sure if I'm doing this correct, god this is tough lol

What am I doing wrong? And why does the chance of getting another head in a row get less an less probable despite having a 50/50 chance?

**EDIT** I just googled to see what the answer is and for 10 heads with 10 flips the probability is $\displaystyle \frac{1}{1024}$ but I can't figure out the formula.

*EDIT** also just googled for 100 heads with 100 flips and the insane answer is $\displaystyle 7.88644\times 10^{-31}\%$ or $\displaystyle \frac{1}{126,799,924,934,444,438,921,525,105,176,6 10}$ lol that is insane!