PROBLEM 1 : What is 1+2+3+.....+141?

We first calculate the sum 1+2+3+....+138+139+140:

1+140 = 141

2+139 = 141

3+138 = 141

....................

70+71 = 141

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70 x 141 = 141 x 70 = 141 x 7 x 10 = (100+40+1) x 7 x 10 =

(700+280+7) x 10 = 987 x 10 = 9870.

Now you still have to add the last number:

9870+141 = 9870+30+111 = 9900+111 = 9900+100+11= 10000+11,

which is 10 011.