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find-unit-digit-of-1-2-3-4-5-100-




Question Number 117007 by TANMAY PANACEA last updated on 08/Oct/20
find unit digit of  1!+2!+3!+4!+5!+....+100!
$${find}\:{unit}\:{digit}\:{of} \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+\mathrm{5}!+….+\mathrm{100}! \\ $$
Answered by mindispower last updated on 08/Oct/20
if n≥5 n!=0(10)  1+2!+3!+4!=24+6+4+1=35  unite 5
$${if}\:{n}\geqslant\mathrm{5}\:{n}!=\mathrm{0}\left(\mathrm{10}\right) \\ $$$$\mathrm{1}+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!=\mathrm{24}+\mathrm{6}+\mathrm{4}+\mathrm{1}=\mathrm{35} \\ $$$${unite}\:\mathrm{5} \\ $$
Commented by TANMAY PANACEA last updated on 08/Oct/20
it is a tricky qustetion who face it first time
$${it}\:{is}\:{a}\:{tricky}\:{qustetion}\:{who}\:{face}\:{it}\:{first}\:{time} \\ $$
Commented by bemath last updated on 09/Oct/20
why not 24+6+2+1=33 ?   unit digit 3
$$\mathrm{why}\:\mathrm{not}\:\mathrm{24}+\mathrm{6}+\mathrm{2}+\mathrm{1}=\mathrm{33}\:?\: \\ $$$$\mathrm{unit}\:\mathrm{digit}\:\mathrm{3}\: \\ $$
Commented by malwaan last updated on 09/Oct/20
unit digit is 3
$${unit}\:{digit}\:{is}\:\mathrm{3} \\ $$
Commented by TANMAY PANACEA last updated on 09/Oct/20
yes
$${yes} \\ $$

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