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I have a doubt in this question. The question is “ Find the value of (1 +1/2)(1+1/3)(1+1/4).....(1+1/120)

I have a doubt in this question. The question is “ Find the value of (1 +1/2)(1+1/3)(1+1/4).....(1+1/120)

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Grade:8

1 Answers

Avishek Bhagat
askIITians Faculty 71 Points
one year ago
Dear Student,
According to the series

( 1 + 1 /2 ) = ( 2 + 1 ) / 2 = 3/2

( 1 + 1/3 ) = ( 3 + 1 ) /3 = 4 / 3

( 1 + 1/ 4 ) = ( 4 + 1 ) / 4 = 5 / 4

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.
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( 1 + 1/ 120 ) = ( 120 + 1 ) / 120 = 121 / 120

Therefore ,

(1 + 1/2 ) ( 1 + 1/3 ) ( 1 + 1/4 ) ....( 1 + 1/ 120)

= ( 3/2 ) ( 4/3) ( 5/4 ) ..... ( 121 / 120 )

the terms on numerator and denominator cancel out and after cancellation we get,

= 121 / 2

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