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find-last-digit-of-1-2-3-4-23-and-1-2-3-134-




Question Number 48884 by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18
find last digit of  1!+2!+3!+4!+...+23!  and 1!+2!+3!+...+134!
$${find}\:{last}\:{digit}\:{of} \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+…+\mathrm{23}! \\ $$$${and}\:\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+…+\mathrm{134}! \\ $$
Answered by mr W last updated on 29/Nov/18
last digit of n! is 0 for n≥5.  1!+2!+3!+4!=33  ⇒last digit of Σ_(k=1) ^n k! is always 3 with n≥5.
$${last}\:{digit}\:{of}\:{n}!\:{is}\:\mathrm{0}\:{for}\:{n}\geqslant\mathrm{5}. \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!=\mathrm{33} \\ $$$$\Rightarrow{last}\:{digit}\:{of}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}!\:{is}\:{always}\:\mathrm{3}\:{with}\:{n}\geqslant\mathrm{5}. \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18
thank you sir... i have posted this question as  it is a tricky question...
$${thank}\:{you}\:{sir}…\:{i}\:{have}\:{posted}\:{this}\:{question}\:{as} \\ $$$${it}\:{is}\:{a}\:{tricky}\:{question}… \\ $$
Commented by mr W last updated on 29/Nov/18
nice question!
$${nice}\:{question}! \\ $$

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