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Which of the following is larger? 9950 + 10050 or 10150 - Mathematics

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प्रश्न

Which of the following is larger? 9950 + 10050  or 10150

बेरीज
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उत्तर

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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पाठ 8: Binomial Theorem - Solved Examples [पृष्ठ १३७]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 8 Binomial Theorem
Solved Examples | Q 13 | पृष्ठ १३७

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