Question

is \((a-b)!=a!-b!\) ? ,\( a\geq 1,b\geq 1\)

Answer 1

!
is factorial ?

Answer 2

@hartnn yes

Answer 3

@hartn can you help me with a question after you are done

Answer 4

if its factorial, then that statement is not true

counterexample :
let
a =4, b =3

(4-3)! =1

4! -3! is NOT 1

Answer 5

also if b>a
then that statement is definitely false, as factorial of negative numbers is not defined

Answer 6

so is it true for
\(\Large a>b>1\)

Answer 7

nopes,
even of a>b>1

say a = 5 , b =3

(5-3)! = 2! =2

5! -3! is not 2

infact,
(a-b)! < a!-b!

Answer 8

or i should say
\((a-b)! \le a!-b! \)

except for a,b =1

Answer 9

ok but somehow if i want to convert

\(\Large (a-b)!\implies a!-b!\)

then is their a way to do it

Answer 10

\((a-b)!\)
cannot be simplified

Answer 11

are you trying to telescope something ?

Answer 12

example\(\Large (5-3)!=5!-3!+C\)

Answer 13

whats the original complete question ?

Answer 14

well it was CAT paper today ,
there was a question like that i cant remeber

Answer 15

oh you gave the exam today ? how was it ?

Answer 16

it was easy but tricky ,math section was easy , and time consuming
, even in english section they ask math question

Answer 17

lol yeah data terpretation takes long time ! good to knw you did well :)

Answer 18

yes i learned that a speed basic tricks and common sense needed, i think any could have
solved it but it is very time consuming ,50 questions for 1 hr and 25 min

Answer 19

40% were from number theory

Answer 20

let us know if you recall the exact question :)