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Sequences and Series: JEE Mains 2022 June 29 Shift 1

Medium· Special series (sum of n, n squared, n cubed)· +4 / −1

Let

\{a_n\}_{n=0}^{\infty}

be a sequence such that

a_0=a_1=0

and

a_{n+2}=2a_{n+1}-a_n+1

for all

n\ge0

. Then,

\displaystyle\sum_{n=2}^{\infty}\dfrac{a_n}{7^n}

is equal to :

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