a + (a + 1) + (a + 2) + … + (a + r – 1) = a(a + r – 1)

 
 
a \; + \; (a + 1) \; + \; (a + 2) \; + \; ... \; + \; (a + r  - 1) \; = \; a \cdot (a + r - 1)
 
 
3 + 4 + 5 + 6 = 18 = 3\times 6

15+16+17+...+35 = 525 = 15\times 35

85+86+87+...+204 = 17340  = 85\times 204

493+494+495+...+1189 = 586177 = 493\times 1189

2871+2872+2873+...+6930 = 19896030 = 2871\times 6930

16731+16732+16733+...+40391 = 675781821 = 16731\times 40391

97513+97514+97515+...+235416 = 22956120408 = 97513\times 235416

568345+568346+568347+...+1372105 = 779829016225 = 568345\times 1372105

3312555+3312556+3312557+...+7997214 = 26491211221770
= \; 3312555\times 7997214

19306983+19306984+19306985+...+46611179 =  899921240562957
= \; 19306983\times 46611179

112529341+112529342+112529343+...+271669860 = 30570830315362260
= \; 112529341\times 271669860

655869061+655869062+655869063+...+1583407981
= \; 1038508305678375841
= \; 655869061\times 1583407981

3822685023+3822685024+3822685025+...+9228778026
= \; 35278711540581704598
= \; 3822685023\times 9228778026

22280241075+22280241076+22280241077+...+53789260175
= \; 1198437683944896688125
= \; 22280241075\times 53789260175

129858761425+129858761426+129858761427+...+313506783024
= \; 40711602541832856049200
= \; 129858761425\times 313506783024

756872327473+756872327474+756872327475+...+1827251437969
= \; 1382996048733983114022337
= \; 756872327473\times 1827251437969

4411375203411+4411375203412+4411375203413+...+10650001844790
= \; 46981154054388011500578690
= \; 4411375203411\times 10650001844790

25711378892991+25711378892992+25711378892993+...+62072759630771
= \; 1595976241800309307879826061
= \; 25711378892991\times 62072759630771

149856898154533+149856898154534+149856898154535+...+361786555939836
= \; 54216211067155259437778676588
= \; 149856898154533\times 361786555939836

873430010034205+873430010034206+873430010034207+...+2108646576008245
= \; 1841755200041473446564812020225
= \; 873430010034205\times 2108646576008245

……………………………………………………….
……………………………………………………….

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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