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In the expansion of (x+y)^n, the …

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In the expansion of (x+y)^n, the coefficient of 4th and 13th term are equal. Find n
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Sia ? 6 years, 3 months ago

In the expansion of (x + y)n,
T4 = T3+1 = nC3xn-3 {tex}\times{/tex} y3
and T13 = T12+1 = nC12xn-12 {tex}\times{/tex} y12
We are given that coefficients of 4th and 13th terms are equal.
{tex}\therefore{/tex} nC3 = nC12
{tex}\Rightarrow{/tex} nC3 = nCn-12 [{tex}\because{/tex} nCr = nCn-r]
{tex}\therefore{/tex} n - 12 = 3 {tex}\Rightarrow{/tex} n = 15

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