The finite series is 0 + 1 + 2 + 3 + 4.
Σ(i – 1) = 0 + 1 +2 + 3 + 4 = 10
i = 1
In summation notation it can be written as above.
Formula;
an = an -1 + 1
In summation notation we write
∞
Σ(n – 1) = 0 + 1 +2 + 3 + 4 +…..
n = 1
For the alternating infinite sequence -1, 2, -3, 4, -5, . . ., the formula is
an = (-1)nn
In summation notation we write it as;
∞
Σ(– 1)n n = - 1 +2 - 3 + 4 - …..
i = 1
For the alternating infinite sequence -1, 2, -4, 8, -16, 32, . . .,
the formula is
an = (-1)n (2)n - 1
General Formula:
Sn = (a1 + an) (n) = n (a1 + an)
22
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