The greatest terms of the expansion $(2 x + 5 y)^{13}$ when x = 10, y = 2 is-

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Solution

$\frac{t_{r + 1}}{t_{r}} = \frac{13 C_{r} (2 x)^{13 - r} (54)^{r}}{13 C r - (2 x)^{13 - (r - 1)} (54)^{r - 1}} = \frac{14 - r}{r} (\frac{54}{2 x}) > 1 = \frac{(14 - r)}{r} (\frac{1}{2}) > 1 (14 - r) > 2 r \frac{14}{3} > r r < 4 \frac{2}{3}$
So, the term is $13 C_{4} (2 x)^{9} (54)^{4}$

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