QUIZ: If the sum of the numbers 1 to 100 can be calculated with Carl Gauss′s method, then How do we calculate the sum of the numbers starting from 2 and going up to 100 by twos in an easy way with the same method? Or 2+4+6+8+10+...+100=?


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Question Number 186348 by test1234 last updated on 03/Feb/23

$Q U I Z :$ $I f t h e s u m o f t h e n u m b e r s 1 t o 100 c a n$ $b e c a l c u l a t e d w i t h C a r l {G a u s s}^{'} s m e t h o d,$ $t h e n H o w d o w e c a l c u l a t e t h e s u m o f t h e$ $n u m b e r s s t a r t i n g f r o m 2 a n d g o i n g u p t o$ $100 b y t w o s i n a n e a s y w a y w i t h t h e s a m e$ $m e t h o d ?$ $O r 2 + 4 + 6 + 8 + 10 + . . . + 100 = ?$
Commented by Frix last updated on 03/Feb/23

$2 + 4 + 6 + . . . + 100 = 2 \times (1 + 2 + 3 + . . . + 50)$ $This is too easy$
Commented by ajfour last updated on 04/Feb/23

$1 + 2 + 3 + . . . . . . . . . . + 24 + 25$ $50 + 49 + 48 + . . . . . . . . . + 27 + 26$ $______________________$ $51 + 51 + 51 + . . . . . . . . . . + 51 + 51$ $= 25 \times 51 = 25 (50 + 1) = 1250 + 25$
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