Question

prove 1=0.999 explain breifly

Answer 1

hlw mate,
______________

ur answer,
=============

⬇️⬇️⬇️⬇️⬇️⬇️

number "0.9999..." can be "expanded" as:

0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

In other words, each term in this endless summation will have a "9" preceded by some number of zeroes. This may also be written as:




That is, this is an infinite geometric series with first term a =  9/10 and common ratio r =  1/10. Since the size of the common ratio r is less than 1, we can use the infinite-sum formula to find the value:



So the formula proves that 0.9999... = 1