math question plz help?

Question

hey guyz
if u save one penny today and double the amount saved each day for 30 days ,how much money have you saved at the end of the 30 days (fr example today u save.01,tommorrow u save .02,the next day you save.04etc)
can u plz tell me the $ saved at teh end of 30 days
thanks in advance

Answer 1

Do it in cents then divide by 100 at the end.

Each day your totals go:
1,3,7,15

Which are 2^1 -1; 2^2 - 1; 2^3 - 1, 2^4 - 1...

So after 30 days you'd have 2^30 - 1 cents. Figure this out then divide it by 100.

Answer 2

x + 2x + 4x + 8x...
this is a geometric series (a list of numbers, where each succeeding number is multiplied by a common ratio, and the next one, and so forth.). each number is multiplied by two, then multiplied by two again, until there are thirty numbers.
the sum of all numbers in a geometric series is given by the equation a (1 - r^n) / 1 - r where r is the common ration (in this case, 2) n is the number of elements (30), and a the first term in the series (1 in your example).
the sum looks like this:
1 (1 - 2^30) / 1 - 2
um...you need a caluculator for this. i'm not too sure about this, though, your teacher might have another, better solution.

Answer 3

1st day is 2^0 = 1
2nd day is 2^1 = 2
30tg day is 2^29
and you have to sum them
so the expression is
sigma 2^n where n=0 to 29

Answer 4

1+2+4+8+16+32+64+128+256+512+1024+2048+4096+8192+16284+32568+65136+130272+260544+521088+1042176+2084352+4168704+8337408+16674816+33349632+66699264+133398528+266797056+533594112=?