a few random questions :
1. Given :$\displaystyle 1 + 2 + 3 + ... + n = \frac{n(n+1)}{2}$
(a) Prove this results from first principles.
2. Show from first principles that,$\displaystyle \sum^n_{i=1} x^i = x\frac{1-x^n}{1-x}$
Hence give an expression of $\displaystyle \sum^{n-1}_{i=0} x^i$
3. Let$\displaystyle g(t) = exp$$\displaystyle \{$$\displaystyle \alpha +$ $\displaystyle \beta$$\displaystyle t$$\displaystyle \}$
Given that g(10) = 8.1882 and g(20) = 60.3403, calculate g(15).
4. Consider a function f such that f(11) = 1.234 and f(12)=2.345. Assuming that the function is linear over the interval from 11 to 12, calculate f(11.36).
Someone would please kindly guide me on how to do the questions! Thanks in advance!