sum limits_{ k =0}^6{ }^{51- k } C _3 is equa | vedclass

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Question

$\sum \limits_{ k =0}^6{ }^{51- k } C _3$

$={ }^{51} C _3+{ }^{50} C _3+{ }^{49} C _3+\ldots+{ }^{45} C _3$

$={ }^{45} C _3+{ }^{46} C _3+\ldots

Vedclass · Accepted Answer

${ }^{52} C _4-{ }^{45} C _4$

Vedclass · Answer

$\sum \limits_{ k =0}^6{ }^{51- k } C _3$

$={ }^{51} C _3+{ }^{50} C _3+{ }^{49} C _3+\ldots+{ }^{45} C _3$

$={ }^{45} C _3+{ }^{46} C _3+\ldots \ldots+{ }^{51} C _3$

$={ }^{45} C _4+{ }^{45} C _3+{ }^{46} C _3+\ldots \ldots+{ }^{51} C _3-{ }^{45} C _4$

$\left.={ }^n C _{ r }+{ }^n C _{ r -1}={ }^{ n +1} C _{ r }\right)$

$={ }^{52} C _4-{ }^{45} C _4$

$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to

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