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Question
In the pattern `1/3 + 1/4 + 1/5 +` ..... which fraction makes the sum greater than 1 (first time)? Explain.
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Solution
`1/3 + 1/4 + 1/5`
= `(20 + 15 + 12)/60`
= `47/60 < 1` ...[∵ Numerator < Denominator]
According to the pattern, next number will be `1/6`
∴ `1/3 + 1/4 + 1/5 + 1/6`
= `(40 + 30 + 24 + 20)/120`
= `114/120 < 1` ...[∵ Numerator < Denominator]
Now, according to the pattern, next number after `1/6` is `1/7`
∴ `1/3 + 1/4 + 1/5 + 1/6 + 1/7`
= `(280 + 210 + 168 + 140 + 120)/840`
= `918/840 > 1` ...[∵ Numerator > Denominator]
Hence, `1/7` makes the sum greater than 1 (first time).
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