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

maybe showing the graph would

step-by-step explanation:

-387129 iq

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