Formulas and Rules

Man is eating a cheese pizza, and he is fond of it. On the first day, he eats half of the pizza. On the second day, he eats $\frac{1}{3}$ rd of the remaining part of the pizza. On the third day, he eats ${\frac{1}{4}}^{\mathrm{th}}$ of what is left and $4^{\mathrm{th}}$ day he eats ${\frac{1}{5}}^{\mathrm{th}}$ of what still remains continues eating pizza in the same process of fraction like on the $5^{\mathrm{th}}$ day $\frac{1}{6}$ on 6th day he eats $\frac{1}{7}$ of what remains so on.
Based upon the information given, what would be the correct formula for the fraction of pizza eaten on ${\mathrm{n}}^{\mathrm{th}}$ day?

Represent the following pattern as an algebraic expression.

Area of a triangle with base '$\mathrm{b}$' and the corresponding altitude '$\mathrm{h}$' is

Find the area of the rectangle if the length is $2l^{2}m$  and breadth is $3l{m}^2.$

Find the number of diagonals drawn from vertex A in figure $4$.

Given diagram shows a matchstick pattern of rhombus. Find the general rule that gives the number of matchsticks required for $8^{th}$ pattern.

The given diagram shows a matchstick pattern of the pentagon. Find the general rule that gives the number of matchsticks required for the $4^{th}$ pattern.

Observe the pattern of sides of a square. Find out the number of sides of a square of ${10}^{th}$ pattern.

Given diagram shows a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks required for $3^{rd}$ pattern.

What is the area of triangle if the height and base are $\left(x+1\right)\text{cm} \text{and} \left(x-2\right)$cm?

What is the area of rectangle if the length and breadth are $\left(x+1\right)\text{cm} \text{and} \left(x-2\right)$cm?