Wednesday, 21 May 2014

sequences and series - Find the first term of an arithmetic progression, given the 7th and the 16th terms

I tried to solve this problem by first finding out the common difference by using the formula
$$
\text{common difference} = \frac{T_p-T_q}{p-q}
$$
with $T_7=-1$ and $T_{16}=17$. But now I'm not able to find the first term. I tried out many methods. Please help me out..

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...