3Sir, Should I write the expression in this way:
(1+1/2)(1+1/22)(1+1/24)........
what will happen if you kept multiplying
\\(1+1/2) \\(1+1/2)(1+1/4) \\(1+1/2)(1+1/4)(1+1/16) \\(1+1/2)(1+1/4)(1+1/16)(1+1/256) \\(1+1/2)(1+1/4)(1+1/16)(1+1/256)......
and so on?
would you get a finite number or an infinite one?
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11 Answers
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11we would probably get an infinite one, coz as we can rite d eqn as (1+1/2)(1+1/22)(1+1/24)........the power of 2 will then go on increasing like 24,26,28,210.... !!!!
62yes sunit.. that is what it seems .. first look..
but this is not what is happening here...
[1]
The number is actually finite...
look at what swastika has done..
62Hint: FIrst prove:
(a+b)(a2+b2) = (a4-b4)/(a-b)
Then try to do this again and again in this question to see what you get
30Is the value like this:
2x - 1 2x-1
where x is the number of times we multiply the terms.
P.S.: Sir if the value of x is infinitely large, then the value of the expression will also be infinitely large. So, how do we get a finite solution?
62yes asish. that is the answer...
Now you have to try and show that this is finite and infact 2...
1taking the limits finishes this off , doesn't it ? but i don't think we should use limits , as this is for IX - X
62yes we shouldnt use limits as a phrase.. but as a simple fact.. that the given sum is actually equal to
2 - 12n-1