In the expansion of (1+2x)^30 in ascending powers of x, the ratio of the coefficient of the (r-1) th term to that of the rth term is 7:17. Find the value of r.

The given problem involves the binomial expansion of \((1 + 2x)^{30}\) in ascending powers of \(x\), and we are tasked with finding the value of \(r\), where the ratio of the coefficient of the \((r-1)\)th term to that of the \(r\)th term is \(7:17\).

The general term in the expansion of \((1 + 2x)^{30}\) is given by the binomial theorem:

\[
T_r = \binom{30}{r-1} (1)^{30-(r-1)} (2x)^{r-1} = \binom{30}{r-1} 2^{r-1} x^{r-1}
\]

So the coefficient of the \((r-1)\)th term is:

\[
\text{Coefficient of the } (r-1) \text{th term} = \binom{30}{r-2} 2^{r-2}
\]

And the coefficient of the \(r\)th term is:

\[
\text{Coefficient of the } r \text{th term} = \binom{30}{r-1} 2^{r-1}
\]

We are given that the ratio of the coefficient of the \((r-1)\)th term to that of the \(r\

In the expansion of (1+2x)^30 in ascending powers of x, the ratio of the coefficient of the (r-1)th term to that of the rth term is 7:17. Find the value of r.

Learn how to find the value of r in the binomial expansion of (1+2x)^30, where the ratio of the coefficient of the (r-1)th term to that of the rth term is 7:17. This problem involves the binomial theorem and understanding coefficient ratios. Suitable for advanced high school students.

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