IIT JEE , AIEEE Forum - Mathematics , Algebra

amitanshukumar_1

[1+1/3][1+1/3^2 ][1+1/3^4 ][1+1/3^8 ].......[1+1/3^(2^n ) ]=? Note-[] is not a Greatest integer function.

neeraj_agarwal_1990

we have the property [x+a] = [x] +a if a is an integer

so answer should be 1!!

am i right?

abhujabal

Yaah I am also getting the answer as 1using the same property

sabarish_13

The answer is n as 1 repeats n times. Am i correct?

nadeemoidu

I think the [] brackets refers to multiplication not greatest integer function. otherwise its a stupid question. try to do it if it means multiplication.

nik_gup

the answer is 1 isn't it?

nadeemoidu

Let S=( 1+ 1/3 ) ( 1+ 1/3 ²) ( 1+ 1/3⁴ ) ( 1+ 1/ 3⁸) .....( 1+ 1/3 ^{2^n})

( 1- 1/3) S =( 1-1/3) ( 1+ 1/3 ) ( 1+ 1/3² ) ( 1+ 1/3 ⁴) ( 1+ 1/ 3⁸ ) .....( 1+ 1/3 ^{2^n})

( 2/3) S = ( 1- 1/3² ) ( 1+ 1/3² ) ( 1+ 1/3 ⁴) ( 1+ 1/ 3⁸ ) .....( 1+ 1/3 ^{2^n})

= ( 1- 1/3 ⁴)( 1+ 1/3 ⁴) ( 1+ 1/ 3⁸ ) .....( 1+ 1/3 ^{2^n})

= ( 1- 1/ 3⁸ ).....( 1+ 1/3 ^{2^n})

and so on....

= ( 1- 1/3 ^{2^n})( 1+ 1/3 ^{2^n})
=( 1- 1/3 ^{2^n+1})

S= (3/2)( 1- 1/3 ^{2^n+1})

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