Question

Evaluate the series 4+2+1+.5+.25 to s_10

Answer 1

Ok. What is happening to the next term every time?

Answer 2

it's being multiplied by .5 or divided by 1/2

Answer 3

Right. So you can figure out the 6th, 7th, 8th, 9th, and 10th term (yes, they will get ugly) and then add 'em up.

Answer 4

I got 8.0625. But the answers aren't in decimals, they're all in mixed numbers

Answer 5

(By the way, it's "multiplied by .5 or divided by *2*", not 1/2)

Answer 6

ah yeah, my mistake, sorry haha

Answer 7

in my mind it was "divided in half"

Answer 8

So let's change them into fractions:

4, 2, 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128

Well, they should all have the same denominator:

4 + 2 + 1 + 64/128 + 32/128 + 16/128 + 8/128 + 4/128 + 2/128 + 1/128

You can take it from here.

Answer 9

7+127/128?

Answer 10

Yup. Thanks!

Answer 11

The neat thing is that if you went to s_9, it would be 7 63/64. If you went to s_8, it would be 7 31/32. If you went to s_11, it would be 7 255/256, and so on. Patterns are beautiful.

Answer 12

Always one less from being a whole number. That's pretty cool.