1. Tardigrade
  2. Question
  3. Mathematics
  4. displaystyle∑ r =063 ( n C r / n C r + n C r +1) is equal to (where n =64 )

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\displaystyle\sum_{ r =0}^{63} \frac{{ }^{ n } C _{ r }}{{ }^{ n } C _{ r }+{ }^{ n } C _{ r +1}}$ is equal to (where $n =64$ )

Binomial Theorem

Solution:

$\displaystyle\sum_{r=0}^{63} \frac{{ }^n C_r}{{ }^{n+1} C_{r+1}}=\displaystyle\sum_{r=0}^{63} \frac{r+1}{n+1}=\frac{1}{n+1}(1+2+3 \ldots \ldots 64)$ $=\frac{1}{65} \times\left(\frac{64 \times 65}{2}\right)=32$.