# Thread: [SOLVED] Binomial Theorem help...

1. ## [SOLVED] Binomial Theorem help...

Question:
Expand $\displaystyle (3+5x)^7$ in ascending powers of $\displaystyle x$ up to and including the term in $\displaystyle x^2$. By putting $\displaystyle x=0.01$, find an approximation, correct to the nearest whole number, to $\displaystyle 3.05^7$.

2. Originally Posted by looi76
Question:
Expand $\displaystyle (3+5x)^7$ in ascending powers of $\displaystyle x$ up to and including the term in $\displaystyle x^2$. By putting $\displaystyle x=0.01$, find an approximation, correct to the nearest whole number, to $\displaystyle 3.05^7$.
You've asked for help on a few of these now. What part of it is confusing you? Tell us so we can help you better.
$\displaystyle (3 + 5x)^7 = \sum_{k = 0}^7 {7 \choose k} (3)^{7 - k}(5x)^k = 3^7 + 7 \cdot (3)^6 (5x)^1 + ~...$

You tell me what the next term is.

-Dan

3. Ultimately, in that approximation of $\displaystyle 3.05^7$, you will have to calculate some $\displaystyle (.01a)^b$ for seven different sets of $\displaystyle a$ and $\displaystyle b$.