Infinite sum of reciprocal products

Calculus Level 3

\[\frac 14 + \frac 2{4 \times 7} + \frac 3{4 \times 7 \times 10} + \frac 4{4 \times 7 \times 10 \times 13} + \cdots = \frac 1a \]

Find \(a\).

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