Question

Suppose we have a chessboard (contains 64 quods). In the first quod we put 0.01 € (1 cents) in the
second squod double the previous one and continue this process until the 64th square, how much money we have
put on the board?

Answer 1

Choose between:
a) (263 -1)€
b) 0.01 . (263 -1)€
c) (264 -1)€
d) 0.01 . (264 -1)€

Answer 2

first form the sequence, then, find \(r\) and \(a\)
after that, use series formula

Answer 3

i do not rember anything.. many years since school,,,

Answer 4

1, 2, 4, 8, 16, 32 .....

Answer 5

ok, np :) chess board has how many squares ? 64 right ?

Answer 6

0.01, 0.0001, 0.00000001, 0.0000000000000001...............1,e-128

Answer 7

so, there will be 64 terms in the series :-

\(\large 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, ... \)

Answer 8

careful, it says first square we put 1 cent
second square we put double

Answer 9

so, it must be like this :-

\(\large 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, ...\)
64 terms will be there

Answer 10

you familiar wid geometric series formula, to find sum of terms ?

Answer 11

no i do not rember

Answer 12

me neither... formula is not on top of my head. google and see if u can get the formula

Answer 13

i believe is 0.01 . (2^64 -1)€

Answer 14

thats correct ! how did u get to that ? :)

Answer 15

because the other answers are somehow idiots ;p

Answer 16

it cannot be 263-1

Answer 17

because the other answers are somehow idiots ;p

Answer 18

lol why not, how do u see that hmm

Answer 19

and it cannot be 2^64-1 ;p

Answer 20

because in the last there is no where the 0.01

Answer 21

thats good observation :)

Answer 22

and in the other cannot be 2^63-1

Answer 23

thank you for your help ;p

Answer 24

yes you're right !! np :)

Answer 25

there is a formula for this also :-

\(\large total \ sum = a(\frac{r^n-1}{r-1})\)

a = 1
r= 2
n = 64

Answer 26

thank you..maybe in the future ;p

Answer 27

ha :)