Question

What is summation notation for the series? b. 500+490+480+ . . . . . . . +20+10

Answer 1

The summation notation for the series 500+490+480+ . . . . . . . +20+10 is

$25500-10\sum\limits^{50}_{n=1} {n}$

A summation notation is used to express a long summation into a single notation.

The given series is:

    500+490+480+ . . . . . . . +20+10

This is an arithmetic series with:

a(1) = 500, and

d = 490 - 500 = -10

The last term is a(n) = 10. Find n first by using the nth term formula of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

10 = 500 + (n-1) . (-10)

10 = 500 -10n + 10

10 n = 500

n = 50

Write the explicit formula for the nth term:

a(n) = a(1) + (n-1) . d

a(n) = 500 + (n-1) . (-10)

a(n) = 500 -10n + 10

a(n) = 510 - 10n

The series is the summation notation from n=1 to n = 50

$=\sum\limits^{50}_{n=1} {a(n)}$

$=\sum\limits^{50}_{n=1} {(510-10n)}$

$=\sum\limits^{50}_{n=1} {510} -\sum\limits^{50}_{n=1} {10n}$

$=510\times50-10\sum\limits^{50}_{n=1} {n}$

$=25500-10\sum\limits^{50}_{n=1} {n}$

Learn more about summation notation of a series here:

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