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Rangpur Higher Secondary 2011/4

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Rangpur Higher Secondary 2011/4

Posted: Wed Feb 02, 2011 9:05 pm
by BdMO
Problem 4:
\[(1)_2 + (.1)_2+ (.01)_2+...=?\]
$(A)_b$ signifies that the number $A$ is represented in base $b$.

Re: Rangpur Higher Secondary 2011/4

Posted: Wed Feb 02, 2011 10:23 pm
by leonardo shawon
Its a binary number.

Re: Rangpur Higher Secondary 2011/4

Posted: Thu Feb 03, 2011 9:23 am
by *Mahi*
The answer is -
2
as $(1)_{2}=(1)_{10}$
and $(0.000...01)_{2}=((1/2)^n)_{10}$ when there is $n$ $0$'s in left hand side.
So the answer is $\sum_{n=0 }^{\infty}(1/2)^n=2$
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