What is the absolute value of the numerically greatest term in the expansion of (1+x) ^15 if x=-1/7?
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Answer:
4 is the May be correct answer
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Given : expansion of (1+x)^15, if x= -1/7
To Find : absolute value of numerically greatest term in the expansion
Solution:
(1 + x)¹⁵
a +1 th term
ⁿCₐ(1)ⁿ⁻ᵃ(x)ᵃ
n = 15
(1)ⁿ⁻ᵃ = 1 for each a
= ¹⁵Cₐ(-1/7)ᵃ
a = 0
=> ¹⁵C₀(-1/7)⁰ = 1
a = 1 => - 15/7
a = 2 => 105/49 = 15/7
a = 3 => -455/343 < 2
a = 4 => 1365/7⁴ < 1
and terms keep decreasing
15/7 is the largest term
Hence 15/7 is the correct answer
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