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Question
Which of the following is larger? 9950 + 10050 or 10150
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Solution
We have (101)50 = (100 + 1)50
= `100^50 + 50(100)^49 + (50*49)/(2*1) (100)^48 + (50*49*48)/(3*2*1) (100)^47 +` ......(1)
Similarly 9950 = (100 – 1)50
= `100^50 - 50 * 100^59 + (50*49)/(2*1) (100)^48 - (50*49*48)/(3*2*1) (100)^47 +` ....(2)
Subtracting (2) from (1), we get
10150 – 9950 = `2 50*(100)^49 + (50*49*48)/(3*2*1) 100^47 +` ....
⇒ 10150 – 9950 = `100^50 + 2 (50*49*48)/(3*2*1) 10^47 +` ....
⇒ 10150 – 9950 > 10050
Hence 10150 > 9950 + 10050
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