Sir I wanna ask u a question

If a_n is the digit in the unit place of the no. 1!+2!+3!+...+n!, then

a₈ + a₉ + a₁₀ +...+a₁₆

 

a. 9        b. 18            c. 27          d. 57

Here since we are only interested in digits at units place, so to find the digit at units place for a given series we need to carry sum of digits at units place only and will retain the digit at units place eventually.

 

Further keep in mind that

 

Digit at units place for 1! = 1

 

Digit at units place for 2! = 2

 

Digit at units place for 3! = 6

 

Digit at units place for 4! = 4

 

Digit at units place for 5! = 0

 

Digit at units place for 6! = 0

 

Digit at units place for 7! = 0,

 

and will be zero for n!, where n >4

 

So,  a₈ = digit at units place of the number (1+2+6+4) = 3

Similarly a₉= 3, .... a₁₆= 3

 

or a₈ + a₉ + a₁₀ +...+a₁₆ = 3 + 3 + ....(nine times) = 27