Question

Write out the result of subtracting 1^3+2^3+....+n^3 from 2^3+3^3+....+(n+1)^3

Answer 1

\[= 1^3 - (n+1)^3\]

Answer 2

See these are like:

a + b + c + d + e + f - (b + c +d + e + f+ g)

After subtracting you will get the first and last term..

a - g

Answer 3

\[1 - (n+1)^3 \implies 1- ((n+1) + 3n(n+1)) \implies -3n^2 - 3n - n = -3n^2 - 4n\]

Answer 4

\[= -3n^2 - 4n\]

Answer 5

Getting or not??

Answer 6

sort of

Answer 7

Where you have problem tell me??

Answer 8

why do you only subtract like terms?

Answer 9

See, the terms are like:

1, 8, 27, 64, 125, \(n^3\) - 8, 27, 64, 125, \(n^3\),\((n+1)^3\)

These are the terms of that two sequence:

On subtracting 8, 27 64, 125 and \(n^3\) will cancel..

Right??

Answer 10

but why do we start subtracting 8-8 and not 1-8??