Question
In Exercises $3-12,$ calculate the first four terms of the sequence, starting with $n=1$$$a_{n}=n+(n+1)+(n+2)+\cdots+(2 n)$$
Step 1
We can rewrite this sequence by grouping all the $n$ terms together and all the constant terms together. This gives us $a_{n}=n+n+n+\cdots+n+(1+2+3+\cdots+n)$. Show more…
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In Exercises $3-12,$ calculate the first four terms of the sequence, starting with $n=1$ $$ c_{n}=1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n} $$
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In Exercises $3-12,$ calculate the first four terms of the sequence, starting with $n=1$ $$ b_{n}=\frac{(2 n-1) !}{n !} $$
In Exercises $3-12,$ calculate the first four terms of the sequence, starting with $n=1$ $$ a_{1}=2, \quad a_{n+1}=2 a_{n}^{2}-3 $$
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