Let `E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+……..` upto `50` terms where `[.]` denotes the greatest integer terms then

Question

Let `E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+……..` upto `50` terms where `[.]` denotes the greatest integer terms then

Let `E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+……..` upto `50` terms where `[.]` denotes the greatest integer terms then
A. `E` is divisible by exactly `2` primes
B. `E` is prime
C. `E ge 30`
D. `E le 35`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B::D
For `1 le x le 33`
`(1)/(3) lt (1)/(3) + (x)/(50) lt 1 rArr [(1)/(3) + (x)/(50)] = 0`
for `34 le x le 50`
`1 lt 1/3 + x/50 lt 4/3`
`1 lt [(1)/(3) + (x)/(50)] = 1`
`:. E = 17`

4 views Answered 2023-02-05 15:29