Is there a reason the decimals of 1/49 resembles a 2^x sequence?

>>8538402
because you're missing 2 from 100

>>8538403
What does he mean by this?

>>8538402
Yes. 0.02*49=0.98. 0.0004*49=0.0196. Keep doing this and slowly you build the decimal. Of course it repeats, so at some point your period of two digits will multiply out to just 9's, so not every set of two digits is a power of two.

>>8538402
[2, 4, 8, 16, 32, 64] * 49
= [98, 196, 392, 784, 1568, 3136]
= [100-2,200-4,400-8,800-16,1600-32,3200-64]

Informally, each pair of digits when multiplied by 49 almost fills the gap left by the previous terms.

Note that it starts to fall down at 64 because the next term, 128, is 3 digits. If you try it with 1/499, you get groups of 3 digits and it holds up until 256 (512 becomes 513 because of 1024). Similarly for 1/4999, 1/49999 and so on.

>>8538402
[math]\sum^{\infty}_{k=1}\frac{2^k}{100^k}=\sum^{\infty}_{k=1}\frac{1}{50^k}=\frac{r}{1-r}\ \text{Where r=}\frac{1}{50}\\ \frac{\frac{1}{50}}{\frac{50-1}{50}}=\frac{1}{49} [/math]

File: dafuq.png (47KB, 1216x464px) Image search: [Google]

47KB, 1216x464px

>>8538402
dafuq

>>8538638
oy vey

>>8538646
you can recognize hebrew it seems

Geometric series a=0.02 r=0.02
S∞=a/(1-r) = 0.02/(1-0.02) = 1/49

>>8538599
this. 1/49 is sum of terms (2/100)^k where k is a natural number

>>8538405
49+49 = 100 - 2

>>8538599

neat

wtf? [math]\displaystyle \frac {424823} {13753943}[/math] has the same pattern with 3^x???

>>8539756
Oops, [math]\displaystyle \frac {424823} {13735943}[/math]