Let $(\begin{matrix} n k \end{matrix})$ represents the Combination of 'n' things taken 'k' at a time, then the value of the sum $(\begin{matrix} 9997 \end{matrix}) + (\begin{matrix} 9896 \end{matrix}) + (\begin{matrix} 9795 \end{matrix}) + . . . . . . + (\begin{matrix} 31 \end{matrix}) + (\begin{matrix} 20 \end{matrix})$ equals-

(\begin{matrix} 9997 \end{matrix})

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(\begin{matrix} 10098 \end{matrix})

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(\begin{matrix} 9998 \end{matrix})

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(\begin{matrix} 10097 \end{matrix})

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Solution

The correct option is D $(\begin{matrix} 10097 \end{matrix})$
$^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$
$^{2} C_{0} =^{3} C_{0};^{3} C_{1} +^{3} C_{0} =^{4} C_{1} ⟹^{100} C_{97}$

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Similar questions

(\frac{n}{k})

n

k

(\frac{99}{97}) + (\frac{98}{96}) + (\frac{97}{95}) + . . . . . . . . + (\frac{3}{1}) + (\frac{2}{0})

100^{1} \times 99^{2} \times 98^{3} \times 97^{4} \times \dots 1^{100}

100^{2} - 99^{2} + 98^{2} - 97^{2} . . . . . . . . . - 3^{2} + 2^{2} - 1^{2}

Wages (₹)	:	100	101	103	102	100	99	97	98	96	95
Cost of living	:	98	99	99	97	95	92	95	94	90	91

100^{2} - 99^{2} + 98^{2} - 97^{2} + 96^{2} + 95^{2} + . . . . = S

S = ?

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