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how many irrational terms are there in the expansion of (x^1/2+y^1/8)^100

how many irrational terms are there in the expansion of (x^1/2+y^1/8)^100

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1 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
7 years ago
(r+1)th term will be equal to : 100Cr x^(r/2) y^((100-r)/8)
For rational term: r/2 and (100-r)/8 should be integer,
so, r = 4, 12, 20,...92,100 will give the rational terms.
Its an A.P with first term 4, common difference: 8, and last term = 100.
hence number of terms: 100 = 4 + (n-1)8 which gives n = 13,
total terms will be 100+1 = 101;
so number of irrational terms = 101-13= 88


Thanks and Regards,
Pratik Tibrewal,
askiitians faculty,
BTech, IITG

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