Question

Let $(a_n)^∞_{n=0}$ be a sequence such that a0=a1=0 and $a_{n+2}=2a_{n+1}−a_n+1$ for all n⩾0. Then, $∑^∞_{n=2} \frac{a_n}{7^n}$ is equal to

• A. $\frac{6}{343}$
• B. $\frac{7}{216}$
• C. $\frac{8}{343}$
• D. $\frac{49}{216}$

Answer 1

Answer: (B)

$\frac{7}{216}$

Answer 2

The correct option is(B): $\frac{7}{216}$

an+2 = 2an+1 – an + 1 & a0 = a1 = 0

a2 = 2a1 – a0 + 1 = 1

a3 = 2a2 – a1 + 1 = 3

a4 = 2a3 – a2 + 1 = 6

a5 = 2a4 – a3 + 1 = 10

$\frac{36_s}{49}=\frac{7}{49×6}$

$s=\frac{7}{216}$