Question

Write the sum using summation notation, assuming the suggested pattern continues. 64 + 81 + 100 + 121 + ... + n2 + ...

Answer 1

`\bf \begin{array}{llllllllllllll} 64&+&81&+&100&+&121&+...\\\\ 8^2&&9^2&&10^2&&11^2&... \end{array}\implies \sum\limits_(n=8)^(\infty)\ n^2`

Answer 2

Answer:
`\sum_(n=8)^(\infty)n^2`

Explanation:

The given series is
`64+81+100+121+...+n^2+...`

It can be seen that all the numbers are perfect square.

hence, the given series is of squares and it can be written as

`8^2+9^2+10^2+11^2.......n^2+.....`

If we assuming the pattern continues till infinity , then by using summation the above series will be written as

`8^2+9^2+10^2+11^2.......n^2+.....=\sum_(n=8)^(\infty)n^2`