The value of \sum_{n = 1}^{20} \left[\right. \frac{n \left(\right. n + 1 \left.\right) \left(\right. n + 2 \left.\right) \left(\right. n + 3 \left.\right) \left(\right. n + 4 \left.\right) \left(\right. n + 5 \left.\right)}{6 !} \left]\right. where [k] denotes greatest integer less than or equal to k, is

Engineering

Mathematics

Properties of Binomial Coefficients

Question

The value of $\sum_{n = 1}^{20} [\frac{n (n + 1) (n + 2) (n + 3) (n + 4) (n + 5)}{6!}]$ where [k] denotes greatest integer less than or equal to k, is

²⁷C₇

²⁶C₆

²⁷C₆

²⁶C₇

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$\sum_{n = 1}^{20} [^{n + 5} C_{6}] = \sum_{n = 1}^{20}^{n + 5} C_{6}$

= ⁶C₆ + ⁷C₆ + ....... + ²⁵C₆ = ²⁶C₇