DP Mathematics: Analysis and Approaches Questionbank

Find the common ratio in terms of $a$.

Find the values of $a$ for which the sum to infinity of the series exists.

Find the value of $a$ when $S_{\infty }=76$.

A biased coin is weighted such that the probability, $p$, of obtaining a tail is $0.6$. The coin is tossed repeatedly and independently until a tail is obtained.

Let $E$ be the event “obtaining the first tail on an even numbered toss”.

Find $\text{P}\left(E\right)$.

Show that Chris will never reach the target if his initial deposit is $\$9000$.

Find the first term of the sequence, $u_1$.

Find $S_{\infty }$.

Find the least value of $n$ such that $S_{\infty }-S_n<0.001$.

Given that $p>0$ and $S_{\infty }=3+\sqrt{3}$, find the value of $x$.

Show that $p=\pm \frac{1}{\sqrt{3}}$.

Show that $p=\pm \frac{1}{\sqrt{3}}$.

Hence or otherwise, show that the series is convergent.

Given that $p>0$ and $S_{\infty }=3+\sqrt{3}$, find the value of $x$.

Find an expression for r in terms of θ.

Find the values of θ which give the greatest value of the sum.

The following diagram shows [CD], with length $b\text{ cm}$, where $b>1$. Squares with side lengths $k\text{ cm},k^2\text{ cm},k^3\text{ cm},\dots$, where , are drawn along [CD]. This process is carried on indefinitely. The diagram shows the first three squares.

The total sum of the areas of all the squares is $\frac{9}{16}$. Find the value of $b$.