Grade 12th passAlgebra
find the greatest term in the expansion of (7-5x)^11 when x=2/3
find the greatest term in the expansion of (7-5x)^11 when x=2/3
1 Answer
Arun
Dear Sara
use the formula
n+ 1 / 1 + |a/b| = 12 / (31/10) = 120/31 = 3._____
hence 4th term is greatest
or you can also solve like this
Binomial expansion of (7 - 5 x)¹¹ when x = 2/3
ie., (7 - 10/3)¹¹ = (21 - 10)¹¹ / 3¹¹
ie., (7 - 10/3)¹¹ = (21 - 10)¹¹ / 3¹¹
We consider the binomial expansion of (21 - 10)¹¹.
In the expansion alternate terms are negative. So we take only positive terms.
21¹¹, ¹¹C₂ 21⁹ 10², ¹¹C₄ 21⁷ 10⁴, ¹¹C₆ 21⁵ 10⁶, ¹¹C₈ 21³ 10⁸, ¹¹C₁₀ 21 10¹⁰
We take ratios of T0/T2, T2/T4, T4 / T6 ... Then we find that 21²/10² is there in every ratio. Its value is 4.41. These ratios are:
4.41/55, 4.41/6 , 4.41*5/7, 14/5, 15
So T0 T6, T6 > T8, T8 > T10
So T4 is maximum. It is ¹¹C₄ 21⁷ 10⁴ / 3¹¹
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