IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

computer001

bhatt sir isnt it sigma(1 to n) where n tends to infinity

sandeepramesh

i dont get why it shouldnt be rational maybe

Bcos the summation is done over rational terms only right? Then why shouldnt the sum be rational only?

amaron

What is given is a non recurring,non terminating decimal .
Hence not a rational number.

Note that sum of infinite rational terms need not be rational.

e^x = 1 +x +x² /2! ....

is obviously not rational even for rational values of x.

That solves the problem!

sandeepramesh

Is that so mr bhatt

but i think its only lim n----> infinity n not infinity itself so its still a finite number of terms making it rational maybe

hsbhatt

nice work amaron.

I mixed it up a little, it is of course a sum to infinite terms.

If you write it down it looks like 0.100100001..., this is a non-terminating, non-recurring decimal representation, which is typical of an irrational number

sandeepramesh

oh yes nice :)

hsbhatt

I simplified the question a bit. The original one had a +ve integer k instead of 10.

Then too the result hold, for in base k, it will read 0.100100001...

I thought it was a lovely concept to bring here

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