It the sum of binomial coefficients in the expansion $(1 + x)^{n}$ is $1024$ the what is the largest coefficient in expansion

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Solution

As we know that, sum of binomial coefficient is $2^{n}$ .
$∴ 2^{n} = 1024$
$\Rightarrow 2^{n} = 2^{10} \Rightarrow n = 10$
Middle term $= T_{\frac{n + 2}{2}} = T_{\frac{10 + 2}{2}} = T_{6}$
$∴ T_{6} =^{10} C_{5} 1^{5} x^{10 - 5} = 252 x^{5}$
Largest coefficient in the expansion $= 252$

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It the sum of binomial coefficients in the expansion (1+x)n is 1024 the what is the largest coefficient in expansion

As we know that, sum of binomial coefficient is 2n.∴2n=1024⇒2n=210⇒n=10Middle term =Tn+22=T10+22=T6∴T6=10C515x10−5=252x5Largest coefficient in the expansion =252

It the sum of binomial coefficients in the expansion $(1 + x)^{n}$ is $1024$ the what is the largest coefficient in expansion

As we know that, sum of binomial coefficient is $2^{n}$ .
$∴ 2^{n} = 1024$
$\Rightarrow 2^{n} = 2^{10} \Rightarrow n = 10$
Middle term $= T_{\frac{n + 2}{2}} = T_{\frac{10 + 2}{2}} = T_{6}$
$∴ T_{6} =^{10} C_{5} 1^{5} x^{10 - 5} = 252 x^{5}$
Largest coefficient in the expansion $= 252$