The value of 2121 C1-10 C1-21 C 2-10 C 2-21 C 3-10 C 3-21 C 4-10 C 4-21 C 10-10 C 10 isA- 221-211B- 220-29C 221-210D- 220-210

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Sum of coefficients of all terms

The value of ...

Question

The value of $(^{21} C_{1} -^{10} C_{1}) + (^{21} C_{2} -^{10} C_{2}) + (^{21} C_{3} -^{10} C_{3}) + (^{21} C_{4} -^{10} C_{4}) + . . . + (^{21} C_{10} -^{10} C_{10})$ is

2^{21} - 2^{11}

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2^{21} - 2^{10}

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2^{20} - 2^{9}

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2^{20} - 2^{10}

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(^{21} C_{1} -^{10} C_{1}) + (^{21} C_{2} -^{10} C_{2}) + (^{21} C_{3} -^{10} C_{3}) + (^{21} C_{4} -^{10} C_{4}) + \dots + (^{21} C_{10} -^{10} C_{10})

(21 C_{1} - 10 C_{1}) + (^{21} C_{2} - 10 C_{2}) + (21 C_{3} - 10 C_{3}) + (21 C_{4} - 10 C_{4}) + \dots . + (21 C_{10} - 10 c_{10})

3^{1} \times^{10} C_{1} + 3^{2} \times^{10} C_{2} + 3^{3} \times^{10} C_{3} + . . . . + 3^{10} \times^{10} C_{10} =

\frac{1}{2}

^{10} C_{0} -

^{10} C_{1} +

2 \cdot^{10} C_{2} -

2^{2} \cdot^{10} C_{3}

2^{9} \cdot^{10} C_{10}

^{10} C_{1} +^{10} C_{2} +^{10} C_{3} + . . . +^{10} C_{9}

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