Question

Which represents the series in sigma notation: 1 + 1/2 + 1/4 + 1/16 + 1/32 + 1/64
Choices in replies

Answer 1

@larryboxaplenty

Answer 2

Hello!

So, if we rewrite the summation terms a bit, I bet you'll be able to see the pattern yourself.

Take a look at it if I write it this way:

\[\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64}\]

Do you see a pattern?

Answer 3

I think there is a term missing, as well.

Answer 4

multiplying by 2

Answer 5

Ok! So each term, we multiply by 2 in the denominator. This is the same as multiplying the entire thing by 1/2.

Now, the first term is 1. Do we know of a way to make it so that:

\[(\frac{1}{2})^a = 1\]

Answer 6

multiply it by 2

Answer 7

Or raise it to the zero power.

Answer 8

So, let's go with raising it to the zero power. That makes the first entry "1."

The next entry is 1/2, which is just 1/2 raised to the first power.

Then 1/4, which is 1/2 squared.

Then 1/8, which is 1/2 cubed.

Right?

Answer 9

Yes

Answer 10

Ok, so when i = 1, we were raising 1/2 to the 0 power.

When i = 2, we raised 1/2 to the power of 1.

i = 3, power of 2

i = 4, power of 3.

What is the relationship between the power and the value of i?

Answer 11

exponent = i-1

right?

Answer 12

Yes