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If a = underset(55 "times")underbrace(11...

If `a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3)+10^(4) and c=1+10^(5)+10^(10)+.+10^50` then prove that a=bc

A

a+b+c

B

a=bc

C

b=ac

D

c=ab

Text Solution

Verified by Experts

The correct Answer is:
B
`a=1+10+10^(2)+….+10^(54)`
`=(10^(55)-1)/(10-1)=(10^(55)-1)/(10^(5)-1)xx(10^(5)-1)/(10-1)=bc`
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