Question 737267
You have


2 parents


4 grandparents (2*2 = 4)


8 great-grandparents (2*2*2 = 8 ... each generation going back doubles the previous count)


16 great-great-grandparents (2*2*2*2 = 16)


32 great-great-great-grandparents (2*2*2*2*2 = 32)


64 great-great-great-great-grandparents (2*2*2*2*2*2 = 64)


Add up the individual counts:


2+4+8+16+32+64 = <font color="red">126 ancestors</font>



Shortcut:


You can take the shortcut and sum the geometric sequence 1*2^(n-1) from n = 1 to n = 6 (since you're going back 6 generations), then subtract off 1 since you're not counting yourself as an ancestor (of you). You would use the formula below and plug in a = 1, r = 2 and n = 6



S = a*(1-r^(n+1))/(1-r)


S = 1*(1-2^(6+1))/(1-2)


S = 1*(1-2^7)/(1-2)


S = 1*(1-128)/(1-2)


S = 1*(-127)/(-1)


S = 127


So if you summed up 1, 2, 4, 8, 16, 32, 64, then you would get 127...BUT you are NOT including yourself in this ancestor list. So you subtract 1 to get 127 - 1 = 126


So either way, there are <font color="red">126 ancestors</font> total.