A crocus fest at Lilac Tree

Including white ones with halos. I’ve never seen anything like it. It isn’t the camera. Or if it is, it’s my eyes too.

The snowdrop battalion still marches down the garden

But crocuses – or croci if you prefer – are out in all colours.

It’s not just snowdrops and crocus. The winter pansies are holding their own

Along with these things – the ones whose name I can never remember – something-anthemum I think.

The daffodils are poised too.

We are not free of the threat of snow which would not be good news, yet they come back in greater numbers every year so maybe we shouldn’t worry.

How to add a sequence of numbers at lightning speed

The usual starting place is to add the numbers from 1 to 100. This is a good one to demonstrate the technique.

Imagine you were to write out all the numbers from zero to 100 in a long line.

0 ... 1 ... 2 ... 3 ... ... 98 ... 99 ... 100

Then underneath these, write the same sequence backwards – 100 down to zero.

100 ... 99 ... 98 ... ... 3 ... 2 ... 1 ... 0

Now you have 1 to 100 written twice (with a couple of zeros) so if you add all this lot together, you will have double the answer you want.

Each pair of numbers (0 + 100, 1 + 99, 2 + 98 etc) adds up to 100.

There are 101 pairs. I.e. 101 lots of 100, which is a simple sum. 100 times 101 is 10100.
Divide by 2 to get the answer you are looking for, which is 5050.

Generally, the sum of any sequence of whole numbers from 1 to x is
x (x + 1) / 2

If you don’t want to start at 1, then it’s not so simple, but I’m not going into that here.