# we want the following:
# #  \sum_{i=0}^{N} \left ( 1-\frac{1}{64^{5}} \right )^i \cdot \frac{1}{64^{5}}
# see http://pier4r.wikidot.com/pierworks:articles:obscurity-could-be-secure

# excel breaks, online calculators break too somehow (it would be nice to just use sum)
# therefore employing at first bc + bash, other possibilities are awk or other more equipped languages.

# echo "scale=32; (1 - 1 / 64^5)^0 * ( 1 / 64^5) " | bc
# .00000000093132257461547851562500


# update 2022-11-27
# Bash is ok, awk could be better in some cases. Surely both could be heavily extended by bc
# but bc on its own is quite powerful in theory, if one writes libraries for it.
# https://www.gnu.org/software/bc/manual/html_mono/bc.html
# http://phodd.net/gnu-bc/
# so let's go full bc

# usage as of 2022-11-27:
# bc -l -q sum_probabilities_base_64.bc , then press enter and get the result (or use the quit command)
# time bc sum_probabilities_base_64.bc for the timings.

define formula (exponent) {
  return (1 - 1 / 64^5)^exponent * ( 1 / 64^5)
}

scale=32
"attempts? (+1):" ; attempts = read()
sum=0
for (i = 0; i <= attempts; i++ ){
    sum += formula(i)
}
"sum:"; sum #leave sum as output
quit