For this one, we need some parameters.
Give yourself 1 minute. No calculator. Pen and paper only.
(FYI I solved this when I was 16 years old, under exam conditions, without a calculator and without any working paper. And it was a little harder than what I set out below, but I set out this problem more as an example of pattern recognition, because that is how I solved it reasonably quickly.)
1^3 + 2^3 + 3^3 + .... 10^3 = ?
The hint is in the subject title. Pattern recognition.
Riddle 5 (Pattern recognition)
Ok and the answer. Which should be apparent from a bit of pattern recognition, at least that is how I worked it out.
Notice that 1+8 = 9. And that this is the sum of (1+2)^2
Notice that 1+8+ 27 = 36. And that is the sum of (1+2+3)^2
And now this is a good party trick (at a boring party) with a pen and paper versus someone with a calculator. Perhaps scale up to 50 or so.
To sum numbers 1 + 2 + 3 ..... + n = (n*(n+1))/2
ie multiply by the next biggest number and divide by 2.
Then it just a matter of squaring the result.
Much easier than summing cubes, your mate (unless I'm at the party) with the calculator may be up to about 10 at most by the time you've completed pretty much for any n.
Notice that 1+8 = 9. And that this is the sum of (1+2)^2
Notice that 1+8+ 27 = 36. And that is the sum of (1+2+3)^2
And now this is a good party trick (at a boring party) with a pen and paper versus someone with a calculator. Perhaps scale up to 50 or so.
To sum numbers 1 + 2 + 3 ..... + n = (n*(n+1))/2
ie multiply by the next biggest number and divide by 2.
Then it just a matter of squaring the result.
Much easier than summing cubes, your mate (unless I'm at the party) with the calculator may be up to about 10 at most by the time you've completed pretty much for any n.