Let us consider the binomial expression \( (1+x)^{n}=\sum_{r=0}^{n} a_{r} x^{r} \), \( \mathrm{P...

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Let us consider the binomial expression \( (1+x)^{n}=\sum_{r=0}^{n} a_{r} x^{r} \),
\( \mathrm{P} \) where \( a_{4}, a_{5} \) and \( a_{6} \) are in \( A P,(n10) \). Consider another

W. binomial expression of \( A=(\sqrt[3]{2}+\sqrt[4]{3})^{13 n} \), the expression of \( A \) contains some rational terms \( T_{a_{1}}, T_{a_{2}}, T_{a_{3}}, \ldots, T_{a_{m}} \) \( \left(a_{1}a_{2}a_{3}\ldotsa_{m}\right) \)
The value of \( \sum_{i=1}^{n} a_{i} \) is
(a) 63
(b) 127
(c) 255
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