41-3-42-3-43-3-59-3-Find-the-last-three-digits-of-the-number-

Question Number 147661 by mathdanisur last updated on 22/Jul/21

41^{3} + 42^{3} + 43^{3} + \dots + 59^{3}

F i n d t h e l a s t t h r e e d i g i t s o f t h e

n u m b e r

Answered by nimnim last updated on 22/Jul/21

S = (1^{3} + 2^{3} + 3^{3} + \dots . + 59^{3}) - (1^{3} + 2^{3} + 3^{3} + \dots . + 40^{3})

= {(\frac{59 \times 60}{2})}^{2} - {(\frac{40 \times 41}{2})}^{2}

= {(1770)}^{2} - {(820)}^{2}

= (. . 70 - . . 20) (. . 70 + . . 20) \to l a s t t w o d i g i t s

= . . 50 \times . . 90

= \dots . 500 \to l a s t t h r e e d i g i t s

Commented by mathdanisur last updated on 23/Jul/21

S i r, (\frac{59 \cdot 60}{2}) - \dots c a n y o u e x p l a i n t h i s

p a r t p l e a s e . ? h o w d i d y o u g e t i t . ?

Commented by mathdanisur last updated on 22/Jul/21

t h a n k s S i r

Commented by mathdanisur last updated on 23/Jul/21

{(\frac{59 \cdot 60}{2})}^{2} - \dots