Question

What is s10 for 1 + 2 + 4 + 8+... 256 511 1023 2047

Answer 1

Answer:

1023

Step-by-step explanation:

$S_n = \dfrac{a(1 - r^n)}{1 - r}$

a = first term

r = common ratio

n = number of terms

Here we have

a = 1

r = 2

n = 10

$S_{10} = \dfrac{1(1 - 2^{10})}{1 - 2}$

$S_{10} = \dfrac{1 - 1024}{-1}$

$S_{10} = \dfrac{-1023}{-1}$

$S_{10} = 1023$

Of course, since 10 is not such a large number of terms, you can simply do this:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023