Question

Evaluate binomial sum involving $\sum C_r \frac{2^r}{r+1}$ for $n=10$.}

• A. $\frac{3^{11}-1}{11}$
• B. $\frac{3^{11}-1}{22}$
• C. $\frac{3^{10}-1}{22}$
• D. $\frac{3^{10}-1}{11}$

Hint:

Use integration trick for binomial denominators.

Answer 1

The Correct Option is B

Step 1: Use identity: \[ \sum \frac{C_r x^r}{r+1}=\frac{(1+x)^{n+1}-1}{(n+1)x} \]
Step 2: Put $x=2$: \[ \frac{3^{11}-1}{11\cdot 2} \]
Step 3: \[ =\frac{3^{11}-1}{22} \]