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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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