Question

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

8 + 27 + 64 + 125 + ... + n^3

Answer 1

my answer-

Answer 2

plugin n = 2,
do you get the first term, 8 ?

Answer 3

no..

Answer 4

\(\large (n-1)^3\)

plugin \(n=2\), what do u get ?

Answer 5

1

Answer 6

so it should be n^3

Answer 7

where n=2

Answer 8

So \(\large \sum \limits_{n=2}^{\infty} (n-1)^3 \) is not a correct representation for the given series

Answer 9

what are the other options ?

Answer 10

it is written

Answer 11

sorry my internet is a little slow

Answer 12

wouldnt it be this? @ganeshie8

Answer 13

\[8+27+64+....+n^3=2^3+3^3+4^3+....+n^3\]
\[=1^3+2^3+3^3+...+n^3-1^3=\sum n^3-1=\left( \sum n \right)^2-1\]
\[=\left( \frac{ n \left( n+1 \right) }{ 2 } \right)^2-1\]

Answer 14

i sent that through and it was wrong..

Answer 15

why wouldnt mine be right?

Answer 16

thats the correct sum notation, but the upper limit has a mistake.

Answer 17

\(\large \sum \limits_{n=2}^{\color{red}{\infty}} n^3 \)

Answer 18

Notice that the given sequence is FINITE, so upper limit has to be "n"

Answer 19

yeah that makes sense

Answer 20

thank you so much

Answer 21

Here is the correct sum notation :

\(\large \sum \limits_{i=2}^{\color{red}{n}} i^3 \)

Answer 22

if i get the question wrong multiple times, it gives me options and this is what it gave me. I am gonna go with A @ganeshie8

Answer 23

yes \(a\) is the only best option among the given options :)

Answer 24

yay (: