Write each series as a Summation in Sigma Notation?

First question:

1/2 + 1/4 + 1/8 + 1/16 = 15/16

Second question: 

1/12 + 2/11 + 3/10 + 4/9 + 5/8 + 6/7 = 69071/27720

Notice this pattern:

(1/2)^1 = 1/2

(1/2)^2 = 1/4

(1/2)^3 = 1/8

(1/2)^4 = 1/16

We want to add those 4 terms (k = 1 to 4):

4

∑ ... (1/2)^k

k=1

UPDATE:

Generally it's a poor idea to try to slip another question into your update. Most people won't see it after they have answered the question. And you essentially get to ask two questions for the price of one. Consider asking your questions separately in the future.

I'll be nice and help you out this time.

Let's write a table of terms, but split it by numerator and denominator:

n | numerator | denominator

1 | 1 | 12

2 | 2 | 11

3 | 3 | 10

4 | 4 | 9

5 | 5 | 8

6 | 6 | 7

Clearly the numerator is the same as n.

The numerator and denominator add to be 13:

n + d = 13

So we could also say the denominator is:

d = 13 - n

There's your pattern:

n | numerator | denominator

n | n | (13 - n)

We want 6 terms (n = 1 to 6)

6

∑ ... n / (13 - n)

n=1 

Do you see why?

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