Rangpur Higher Secondary 2011/4

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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Joined: Tue Jan 18, 2011 1:31 pm

Rangpur Higher Secondary 2011/4

Problem 4:
$(1)_2 + (.1)_2+ (.01)_2+...=?$
$(A)_b$ signifies that the number $A$ is represented in base $b$.

leonardo shawon
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Location: Dhaka

Re: Rangpur Higher Secondary 2011/4

Its a binary number.
Ibtehaz Shawon
BRAC University.

long way to go .....

*Mahi*
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Re: Rangpur Higher Secondary 2011/4

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 $\sum_{n=0 }^{\infty}(1/2)^n=2$
Use $L^AT_EX$, It makes our work a lot easier!