The largest coefficient in (1 + x)

Question:

The largest coefficient in (1 + x)30 is ___________.

Solution:

for $(1+x)^{30}$

$T_{r+1}={ }^{n} C_{r}(1)^{30-r} x^{r}$

Since $n=30 \quad$ i.e. $\quad$ even

The largest coefficient is fo $r r=\frac{n}{2}=15$

i.e for middle term

which is 30C15.

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