The sum 21 10C0− 10C1+ 2⋅ 10C2− 22⋅ 10C3+...+29⋅ 10C10 is equal to

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The sum {1}{2} ^{10}{C}_{0}- ^{10}{C}_{1}+ 2 ^{10}{C}_{2}- 2^

Question

The sum $\frac{1}{2}$ $^{10} C_{0} -$ $^{10} C_{1} +$ $2 \cdot^{10} C_{2} -$ $2^{2} \cdot^{10} C_{3}$ +...+ $2^{9} \cdot^{10} C_{10}$ is equal to

\frac{1}{2}

0

\frac{1}{2} \cdot 3^{10}

none of these

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Daniel Discussed

The sum

\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}

is equal to

15 mins ago

Discuss this question LIVE

15 mins ago

Let

S_{n} = \frac{1}{2}^{10} C_{0} -^{10} C_{1} + ...^{10} C_{10} 2^{9}

2 S_{n} =^{10} C_{0} - 2^{10} C_{1} + 2^{2}^{10} C_{2} + ...^{10} C_{10} 2^{10}

2 S_{n} = (1 - 2)^{10}

2 S_{n} = (1)

S_{n} = \frac{1}{2}

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Question Text	The sum $\frac{1}{2}$ $^{10} C_{0} -$ $^{10} C_{1} +$ $2 \cdot^{10} C_{2} -$ $2^{2} \cdot^{10} C_{3}$ +...+ $2^{9} \cdot^{10} C_{10}$ is equal to
Answer Type	Text solution:1
Upvotes	150