Question

Write the sum using summation notation, assuming the suggested pattern continues. 16 + 25 + 36 + 49 + ... + n2 + ...

Answer 1

$\bf \stackrel{4^2}{16}+\stackrel{5^2}{25}+\stackrel{6^2}{36}+\stackrel{7^2}{49}+...\qquad \qquad \qquad \sum\limits_{i=4}^{\infty}~i^2$

Answer 2

Answer:

Hence, the sum using summation notation, assuming the suggested pattern continues $16+25+36+49+......+n^2+.....$ is:

$\sum_{n=4}^{\infty}n^2$

Step-by-step explanation:

We have to write the sum using summation notation, assuming the suggested pattern continues:

$16+25+36+49+......+n^2+.....$

Clearly we may also write this pattern as:

$4^2+5^2+6^2+.....+n^2+......$

So, in terms of the summand it is written as:

$\sum_{n=4}^{\infty}n^2$

( We have started our summation from 4 since the term in the summation starts with 16 which is 4^2 and goes to infinity )