solve it now guys and help me
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jhumakardeb:
PLZ ANSWER THE LAST QUESTION ASKED BY ME PLZ
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Hey...!! HERE IS YOUR ANSWER...!!
First of all, when you see this sort of seemingly intractable problem, don't despair. There's usually a very simple "trick" that makes the problem trivial.
In this case, you have to realise two things:
1) only the sum of last digits contributes to the last digit of the final sum.
2) factorials of larger numbers have a lot of zeroes at the end.
So your problem reduces to deciding the final term you have to consider. Luckily this is a very easy problem. Because:
5!=1205!=120
6!=7206!=720
and so forth, every factorial after that ending with a zero.
So you only have to consider the sum 1!+2!+3!+4!1!+2!+3!+4!.
Even that's simplified by recognising that 3!3! ends with a 66 and 4!4! with a 44, so they will sum up to give 00 as the last digit.
Turns out all you have to consider is 1!+2!1!+2!, which is just 33.
I wanted to put an exclamation point at the end of the last line to emphasise how easy the whole thing was, but decided not to because it might look like a factorial!
HERE IS YOURS SOLUTION;
◆ 1 ! + 2! + 3! + ...........+ 49!
Now,
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
◆ Now, the last digit of 5! = 0 and also next term has 0 last digit.
Therefore, on adding first four terms, that is, 1+2+6+24=33 and the last digit of 33 is 3.
★ So, the last digit is 3 ★
First of all, when you see this sort of seemingly intractable problem, don't despair. There's usually a very simple "trick" that makes the problem trivial.
In this case, you have to realise two things:
1) only the sum of last digits contributes to the last digit of the final sum.
2) factorials of larger numbers have a lot of zeroes at the end.
So your problem reduces to deciding the final term you have to consider. Luckily this is a very easy problem. Because:
5!=1205!=120
6!=7206!=720
and so forth, every factorial after that ending with a zero.
So you only have to consider the sum 1!+2!+3!+4!1!+2!+3!+4!.
Even that's simplified by recognising that 3!3! ends with a 66 and 4!4! with a 44, so they will sum up to give 00 as the last digit.
Turns out all you have to consider is 1!+2!1!+2!, which is just 33.
I wanted to put an exclamation point at the end of the last line to emphasise how easy the whole thing was, but decided not to because it might look like a factorial!
HERE IS YOURS SOLUTION;
◆ 1 ! + 2! + 3! + ...........+ 49!
Now,
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
◆ Now, the last digit of 5! = 0 and also next term has 0 last digit.
Therefore, on adding first four terms, that is, 1+2+6+24=33 and the last digit of 33 is 3.
★ So, the last digit is 3 ★
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