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

Question

anonymous · Answer

$$= 1^3 - (n+1)^3$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

$$= -3n^2 - 4n$$

anonymous · Answer

Getting or not??

anonymous · Answer

sort of

anonymous · Answer

Where you have problem tell me??

anonymous · Answer

why do you only subtract like terms?

anonymous · Answer

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??

anonymous · Answer

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

anonymous · Answer

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