Video: Expressing a Given Series in Sigma Notation

Express the series 8 + 32 + 72 + 128 + ... + 512 in sigma notation.

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Video Transcript

Express the series eight plus 32 plus 72 plus 128 and so on, all the way up to 512, in sigma notation.

In order to express any series using sigma notation, we need to write it in the form the sum of 𝑒 sub π‘Ÿ where π‘Ÿ takes values from one to 𝑛. We need to work out the expression for 𝑒 sub π‘Ÿ, which is the general term of the series. At first glance, there doesn’t appear to be an obvious link between each of the terms in our series. However, they do all have a common factor of eight. Eight is eight multiplied by one, 32 is eight multiplied by four, 72 is eight multiplied by nine, and so on. One, four, nine, 16, and so on are the square numbers. This means that the general term of our series is eight multiplied by π‘Ÿ squared. As eight squared is equal to 64, our lower and upper limits are equal to one and eight.

The given series expressed using sigma notation is the sum of eight π‘Ÿ squared, where π‘Ÿ takes values from one to eight. We could check this answer by substituting in each of our values of π‘Ÿ which would obtain the terms eight, 32, 72, and so on.

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