math

kflowers

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Jun 9, 2010
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find the difference between the sum of the first 100 positive multiples of three and the sum of the first 100 positive even integers.
 
kflowers said:
find the difference between the sum of the first 100 positive multiples of three and the sum of the first 100 positive even integers.

St  =  03  +  06  +  09  +12  ...  +  294  +  297  +300\displaystyle S_t \ \ = \ \ 03 \ \ + \ \ 06 \ \ + \ \ 09 \ \ + 12 \ \ . . . \ \ + \ \ 294 \ \ + \ \ 297 \ \ + 300 ......................(1)

Se  =  02  +  04  +  06  +08  ...  +  196  +  198  +200\displaystyle S_e \ \ = \ \ 02 \ \ + \ \ 04 \ \ + \ \ 06 \ \ + 08 \ \ . . . \ \ + \ \ 196 \ \ + \ \ 198 \ \ + 200.......................(2)

if we subtract (2) from (1) .....continue
 
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