Question

The value of is

• A. 3ⁿ – 1
• B. 3ⁿ + 1
• C. 3ⁿ
• D. 3 (3ⁿ – 1)

Answer 1

Answer: (A)

3ⁿ – 1

Answer 2

= $\sum_{s = 1}^{n}nC_{s}(^{s}C_{0} +^{s}C_{1} +^{s}C_{2}... +^{s}C_{s})$

= $\sum_{s = 1}^{n}nC_{s}2^{s} = \sum_{s = 0}^{n}{nC_{s}2^{s}–^{n}C_{0}2^{0}}$

= (1 + 2)ⁿ – 1 = 3ⁿ – 1