Question

The value of the sum S_rs 2^r3^s, where S_rs = 0, if r ¹ s and S_rs = 1, if r = s :

• A.
• B. $\frac { 6 } { 5 }$ (6ⁿ – 1)
• C.
• D. $\frac { 5 } { 4 }$(5ⁿ – 1)

Answer 1

Answer: (B)

$\frac { 6 } { 5 }$ (6ⁿ – 1)

Answer 2

S_rs 2^r3^s = 2.3 + 2² . 3² + 2³ . 3³ +….+ 2ⁿ . 3ⁿ

(as S_rs = 0, if r ¹ s and S_rs = 1, if r = s)

=

= $\frac { 6 } { 5 }$(6ⁿ – 1).