Question
Download Solution PDFThe sum of all proper fractions whose denominators are less than or equal to 100 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used :
(1 + 2 + 3 + 4 + ......... + 99) = [ n ( n + 1 ) ] ÷ 2
Solution :
We can write all proper fractions whose denominators are less than or equal to 100 in given form :
⇒ 1/2 + (1/3 + 2/3) + (1/4 + 2/4 + 3/4) + ... (1/100 + 2/100 + .. .. 99/100)
⇒ 1/2 + 3/3 + 6/4 + ..... + 4950/100
⇒ 1/2 + 1 + 3/2 + 2 + ........ + 99/2
We can also write this equation in following way :
⇒ 1/2 + 2/2 + 3/2 + ...... + 99/2
⇒ 1/2 ( 1 + 2 + 3 + ..... + 99 )
⇒ /2 [ ( 99 × 100) ÷ 2 ]
⇒ 99 × 25
⇒ 2475
Hence the correct answer is "2475".
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