Question

let x=0.0000......1 then infinity*x =1,is it true

Answer 1

No infinity never terminates and you are terminating it by writing ...1 at last therefore it isn't infinity only " ....." this part is infinity but ...1 not this one!

Answer 2

yes it's true here 0.00.......1 is called infinitesimal
this is smallest no. greater than zero
it can be defined as
0<infinitesimal<n

where n is any other no.
or

1/infinite

when we say 1/infinite people may say
1/infinite =zero

but it isn't true because then
infinite × zero = 1

(it can not happen because any no. ×0 must be equal zero)

hence 1/infinite = infinitesimal

thus infinite × infinitesimal =1

hope it helps