Question

how to find the tens digit of 1!+2!+3!+....9! if we don't know the values of the factorials

Answer 1

Answer:

1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.......+29!

Since,1!+2!+3!+4!=33

After this for 5!,6!,7! all ones place will come 0

Hence ones place of 1!+2!+....29! is 3

But for tens place, the tens place will become 0 for factorial of numbers above 10. Hence, we have to add all the tens places for no.s below 10, which is,

3(till4!)+2(for5!)+2(for6!)+4(for7!)+2(for8!)+8(for9!)

=21

Hence, the tens digit will be 1 and 2 will be carry.

Answer 2

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1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.......+29!

Since,1!+2!+3!+4!=33

After this for 5!,6!,7! all ones place will come 0

Hence ones place of 1!+2!+....29! is 3

But for tens place, the tens place will become 0 for factorial of numbers above 10. Hence, we have to add all the tens places for no.s below 10, which is,

3(till 4!)+2(for 5!)+2(for 6!)+4(for 7!)+2(for 8!)+8(for 9!)

=21

Hence, the tens digit will be 1 and 2 will be carry.