IIT JEE , AIEEE Forum - Mathematics , Algebra

nitish_22691

Solve this & get a salute from me.........

Q- Find the no. in unit place in sum of cofficient of

2 99 103
(1!+2!x+3!x +...........+100!x )

DON007

hey ................look...............

the sum of the coefficient is

1! +2! + 3! + 4! +5! +6! + ................100!

(1+ 2+6+24)+120+720+ ..........and all the no.s ending with 0.............

( 33 )+ 120 + 720+ all the no.s ending with 0.....................

therefore.............

33 + all no.s ending with 0

= 3 ( the unit digit)...........

therefore the no. in unit dihit is 3............

now 3^{103 =} 7 as last digit...................

due to regular patterns followed by 3.................

i think i m right..............

please check it