Find the sum of
$(^{100} C_{0} +^{100} C_{2} +^{100} C_{6} + . . . . .)$

2^{99}

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- 2

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2^{50}

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- 2^{50}

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Solution

The correct option is A $2^{99}$
$W e k n o w t h a t 2^{n - 1} =^{n} C_{0} +^{n} C_{2} +^{n} C_{4} + . . . . . . . . .$

On putting $n = 100$ , we get
$2^{99} =^{100} C_{0} +^{100} C_{2} +^{100} C_{4} + . . . . .$

Hence, the option $A$ is the correct answer

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Similar questions

Q. Find the sum of the given numbers:

\frac{7}{100} + \frac{250}{1000} + \frac{45}{10, 000}

Q. Sum of the series

1 + 2.2 + {3.2}^{2} + . . . . + 100 \times 2^{99}

Q. Find the mean, median and mode of the following data:

Classes:	$0 - 50$	$50 - 100$	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$
Frequency:	$2$	$3$	$5$	$6$	$5$	$3$	$1$

100*(250 $\div$ 25.02) - ? $\times$ 10 = 400

Find the mean, median and mode of the following data:
$\begin{matrix} Class & 0 - 50 & 50 - 100 & 100 - 150 & 150 - 200 & 200 - 250 & 250 - 300 & 300 - 350 Frequency & 2 & 3 & 5 & 6 & 5 & 3 & 1 \end{matrix}$

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Find the sum of (100C0+100C2+100C6+.....)

The correct option is A 299Weknowthat2n−1=nC0+nC2+nC4+.........On putting n=100, we get299=100C0+100C2+100C4+.....Hence, the option A is the correct answer

Find the sum of
$(^{100} C_{0} +^{100} C_{2} +^{100} C_{6} + . . . . .)$

The correct option is A $2^{99}$
$W e k n o w t h a t 2^{n - 1} =^{n} C_{0} +^{n} C_{2} +^{n} C_{4} + . . . . . . . . .$

On putting $n = 100$ , we get
$2^{99} =^{100} C_{0} +^{100} C_{2} +^{100} C_{4} + . . . . .$

Hence, the option $A$ is the correct answer