There is a little sum I am stuck with.

Find the value of $${1 \choose 0}+{4 \choose 1}+{7 \choose 2} +\ldots+{3n+1 \choose n}$$

where ${n \choose r}$ is the usual combination.

A little hint will be fine.

  • $\begingroup$ Are you looking for a closed form of the sum? Because wolfram alpha's is kind of ugly... $\endgroup$ – recursive recursion Jan 18 '15 at 19:36
  • $\begingroup$ Yes a general formula for integer n $\endgroup$ – UNM Jan 18 '15 at 19:40
  • $\begingroup$ I'd go with induction here. $\endgroup$ – barak manos Jan 18 '15 at 19:48
  • $\begingroup$ Please write your steps $\endgroup$ – UNM Jan 18 '15 at 19:49

Find the coefficient of $x^{0}$ in $\displaystyle (1+x)+\frac{(1+x)^{4}}{x}+\frac{(1+x)^{7}}{x^{2}}+\ldots$
It's forming a geometric series.

  • $\begingroup$ Please write your calculations and give me final answer. $\endgroup$ – UNM Jan 19 '15 at 14:57

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