Question

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

343 + 512 + 729 + 1000 + ... + n3

summation of the quantity n minus 1 cubed from n equals 7 to infinity
summation of n cubed from n equals 7 to infinity
summation of n cubed from n equals 8 to infinity
summation of the quantity n plus 1 cubed from n equals 7 to infinity

Answer 1

second sum

Explanation:

Note the given terms are perfect cubes, that is

343 = 7³

512 = 8³

729 = 9³

1000 = 10³

The sequence continues in this way as indicated by the dots ......

The first term is 343 and occurs when n = 7

The sequence is infinite, thus can be expressed as

∑ n³ from n = 7 to infinity