Sequence and series

Question

Let a = 111....1 (55 digits), b= 1+10+10^2..+10^4, c= 1+ 10^5 +10^10 + 10^15 +..... +10^50, then which of the following is correct :

 

1) a=b+c

2)a=bc

3) b=ac

4) c=ab

Answer 1

Tried to comment, but does't seem to be showing up.  (sorry if it does later)

 

c is actually 1000010001...100010001 (51 digits), so a is definitely the biggest of the 3, but adding won't get all the 1's required.

Answer 2

Hi again, Sam.

 

Hope you had a great Saturday.

 

If you just start writing out b and c, you will see the correct answer.

 

b = 1 + 10 + 100 + 1000 + 10000.

 

Line these up vertically instead:

 

      1

     10

    100

  1000

10000

 

This equals

11111.

 

Notice that c = 100000 + 1000000

 

so adding c will put the other 50 1's in front of the 1's that b provides.

 

So the answer is:   a = b + c