The partial sum 1 + 6 + 11 +...+ 106 equals

There are 22 terms in the sum, since there is a difference of 5 between consecutive terms, and 5n + 1 = 1 for n = 0 and 5n + 1 = 106 for n = 21.

Now, if

S = 1 + 6 + 11 + … + 96 + 101 + 106

then it's also true that

S = 106 + 101 + 96 + … + 11 + 6 + 1

Notice that terms in the same position of these two copies of S add up to 107 :

1 + 106 = 107

6 + 101 = 107

11 + 96 = 107

and so on.

If we then combine S with its reverse, we get

2S = 107 + 107 + … + 107 + 107

but the right side consists of 22 terms, so

2S = 107 • 22

S = 107 • 22 / 2

S = 1177

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)

part d

step-by-step explanation:

theresa talked her parents into getting sd cards for her phone and her brother’s phone. inserting an sd card into a phone gives it more storage. they both get 8-gigabyte sd cards. how many bits of storage come with each sd card? type your answer in both scientific and standard notation.