Adding a sequence in the
form: 1 + 2 + ... + n:
A. This
sequence is sometimes referred to as Triangular Numbers,
B. Using
numbers instead of variables we get the following:
1.
Multiply the last number by that number plus 1, then divide by 2.
2. Notice
one of these numbers is divisible by 2, so you can divide the even
number by
2 and then multiply by the other number.
Ex [1] 1
+ 2 + ... + 10 =_________.
a) From
the equation we know this is equal to: 10 x 11/2 or 5 x 11 = 55.
b) The
answer is 55.
Ex [2]
1 + 2 +
... + 50 =_________.
a) From
the equation we know this is equal to: 50 x 51/2 or
25 x 51 =
1275. See Multiplying by 25.
b) The
answer is 1275.
C.
Sometimes there might be a number missing to throw you off, so you need to be
careful.
Ex [3] 2
+ 3 + 4 + ... + 25 =_________.
a) Notice
that the number 1 is missing from the equation. Treat it as though it
were
there.
b) From
the equation we know this is equal to: 25 x 26/2 or 25 x 13 = 325.
c) Since
the number 1 is missing, you should subtract 1 from 325. The
answer is
324.