if i have a list 2, 4, 8,... 2048 how do i find the sum of those numbers?

Answer 1

Figure out the rest of them (there aren't that many) and just add them up on your calculator. Or, use a series formula from your math text.

Answer 2

Your using base 2. So 2^0 = 1, 2^1 = 2, 2^2 = 4, etc. As it turns out, the sum of all numbers in base 2, up to some exponent "n", is equal to (2^n)-1. For instance, 2^0 + 2^1 + 2^2 = 1+2+4 = 7, which is equal to (2^3)-1 = 8-1 = 7. Follow same argument for your set of numbers.

Answer 3

In an Excel spread sheet say Cell A1 type 2. In the next cell say Cell A2 type =2 * Cell A1. Then copy Cell A2 to Cells A3 up to A11. Then type in the next cell address =SUM(A1:A11). This will yield you 4094.

Example: 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 = 4094

Answer 4

2,4,8,16,32,64,..................................2048
2+4+8+16+32+64+.........................+2048=?

2 . . . . . . . . . . . . . . . . . . . . . = {(2) x 2 - 2} = 4 - 2 = 2
2+4 . . . . . . . . . . . . . . . . . . .= {(4) x 2 - 2} = 8 - 2 = 6
2+4+8 . . . . . . . . . . . . . . . . = {(8) x 2 - 2} = 16 - 2 = 14
2+4+8+16 . . . . . . . . . . . . .={(16) x 2 - 2} = 32 - 2 = 34
2+4+8+16+32 . . . . . . . . . ={(32) x 2 - 2} = 64 - 2 = 62
. . . . .
. . . . .
2+4+8+16+32+ .. .+2048={(2048) x 2 - 2} =4096 - 2= 4094

Answer 5

each term is multiply by 2, so the ratio is two

the formula to find the sum of a geomectric sum is:

sum = a1 (1 - r^n) / (1 - r)

a1 = first term
r = ratio
n = position number

the position number of 2048
A_n = a1 (r)^(n-1)

2048 = 2 (2)^(n - 1)
1024 = (2)^(n - 1)
log 1024 = (n - 1) log2
10 = n - 1
n = 11

Sum = 2 (1 - (2^11) ) / (1 - 2)
sum = 4094

Answer 6

the numbers double at each interval the sum of the sequence at any point is equal to the last number doubled minus the first number.
8x2-2=14
2+4+8=14
2048x2-2=4094

Answer 7

This is a GP with a =2, r=2
ar^n-1 = 2048
r^n-1 =1024
n-1 = 10
n=11

Sum of 11 terms = a(1-r^n)/ (1-r)
= 2( 1-2^11) /(1-2)
=2 x2047
=4094

Answer 8

n .... sum
2 .... 2
4 .... 6
8 .... 14
16 .. 30
32 .. 62
64 .......

do you see that the sum is always 2 less than the next number in the series? so the sum of 2 + 4 + 8 + ... + 2048 = 4096 - 2 = 4094.