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Write the sum using summation notation, assuming the suggested pattern continues.

25 + 36 + 49 + 64 + ... + n2 + ...

User Haseoh
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2 Answers

2 votes

Answer:

The sum using summation notation, assuming the suggested pattern continues is :


25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_(n=5)^(\infty) n^2

Explanation:

We are given a series of numbers as

25 + 36 + 49 + 64 + ... + n^2 + ...

To write the sum using summation notation means we need to express this series in terms of a general n such that there is a whole summation expressing this series.

Here we see that each of the numbers could be expressed as follows:


25=5^2\\\\36=6^2\\\\49=7^2\\\\64=8^2

and so on.

i.e. the series starts by taking the square of 5 then of 6 then 7 and so on.

and the series goes to infinity.

Hence, the summation notation will be given by:


25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_(n=5)^(\infty) n^2

User Dannyxnda
by
8.9k points
6 votes

Answer:


\sum_(n=5)^(\infty)n^2

Explanation:

The pattern given is:

25+36+49+64+...+n^2+...

The pattern can be written as

(5)^2+(6)^2+(7)^2+(8)^2+.....+n^2+....

The series is started with 5 and it continues up to infinity.

The summation notation for the given series is:


\sum_(n=5)^(\infty) n^2

n= 1 and goes up to infinity and the series is made up of taking square of n,

User Genadinik
by
7.9k points
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