Binomial Expansion
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Binomial Theorem and its Simple Application

119576 The value of \(\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots . .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}\) is

1 \(\frac{2^{51}}{50 !}\)
2 \(\frac{2^{50}}{50 !}\)
3 \(\frac{2^{51}}{51 !}\)
4 \(\frac{2^{50}}{51 !}\)
JEE Main-01.02.2023
Binomial Theorem and its Simple Application

119577 The value of \(\sum_{n=1}^{13}\left(i^n+i^{n+1}\right)\) where \(i=\sqrt{-1}\) equals

1 0
2 i
3 \(-\mathrm{i}\)
4 i-1
AMU-2016
Binomial Theorem and its Simple Application

119578 Let
\(\mathrm{S}=\frac{\mathbf{2}}{\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_0+\frac{\mathbf{2}^2}{\mathbf{2}}{ }^{\mathrm{n}} \mathrm{C}_1+\frac{\mathbf{2}^3}{\mathbf{3}}{ }^{\mathrm{n}} \mathrm{C}_2+\ldots+\frac{\mathbf{2}^{\mathrm{n}+1}}{\mathrm{n}+\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}}\). The n, \(S\) equals

1 \(\frac{2^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
2 \(\frac{3^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
3 \(\frac{3^{\mathrm{n}}-1}{\mathrm{n}}\)
4 \(\frac{2^n-1}{n}\)
WB JEE-2014
Binomial Theorem and its Simple Application

119579 In the expansion of \((x-1)(x-2) \ldots(x-18)\), the coefficient of \(x^{17}\) is

1 684
2 -171
3 171
4 -342
WB JEE-2016
For More Updates join with Us
Binomial Theorem and its Simple Application

119576 The value of \(\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots . .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}\) is

1 \(\frac{2^{51}}{50 !}\)
2 \(\frac{2^{50}}{50 !}\)
3 \(\frac{2^{51}}{51 !}\)
4 \(\frac{2^{50}}{51 !}\)
JEE Main-01.02.2023
Binomial Theorem and its Simple Application

119577 The value of \(\sum_{n=1}^{13}\left(i^n+i^{n+1}\right)\) where \(i=\sqrt{-1}\) equals

1 0
2 i
3 \(-\mathrm{i}\)
4 i-1
AMU-2016
Binomial Theorem and its Simple Application

119578 Let
\(\mathrm{S}=\frac{\mathbf{2}}{\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_0+\frac{\mathbf{2}^2}{\mathbf{2}}{ }^{\mathrm{n}} \mathrm{C}_1+\frac{\mathbf{2}^3}{\mathbf{3}}{ }^{\mathrm{n}} \mathrm{C}_2+\ldots+\frac{\mathbf{2}^{\mathrm{n}+1}}{\mathrm{n}+\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}}\). The n, \(S\) equals

1 \(\frac{2^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
2 \(\frac{3^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
3 \(\frac{3^{\mathrm{n}}-1}{\mathrm{n}}\)
4 \(\frac{2^n-1}{n}\)
WB JEE-2014
Binomial Theorem and its Simple Application

119579 In the expansion of \((x-1)(x-2) \ldots(x-18)\), the coefficient of \(x^{17}\) is

1 684
2 -171
3 171
4 -342
WB JEE-2016
NEET DIGITAL LIBRARY
Binomial Theorem and its Simple Application

119576 The value of \(\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots . .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}\) is

1 \(\frac{2^{51}}{50 !}\)
2 \(\frac{2^{50}}{50 !}\)
3 \(\frac{2^{51}}{51 !}\)
4 \(\frac{2^{50}}{51 !}\)
JEE Main-01.02.2023
Binomial Theorem and its Simple Application

119577 The value of \(\sum_{n=1}^{13}\left(i^n+i^{n+1}\right)\) where \(i=\sqrt{-1}\) equals

1 0
2 i
3 \(-\mathrm{i}\)
4 i-1
AMU-2016
Binomial Theorem and its Simple Application

119578 Let
\(\mathrm{S}=\frac{\mathbf{2}}{\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_0+\frac{\mathbf{2}^2}{\mathbf{2}}{ }^{\mathrm{n}} \mathrm{C}_1+\frac{\mathbf{2}^3}{\mathbf{3}}{ }^{\mathrm{n}} \mathrm{C}_2+\ldots+\frac{\mathbf{2}^{\mathrm{n}+1}}{\mathrm{n}+\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}}\). The n, \(S\) equals

1 \(\frac{2^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
2 \(\frac{3^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
3 \(\frac{3^{\mathrm{n}}-1}{\mathrm{n}}\)
4 \(\frac{2^n-1}{n}\)
WB JEE-2014
Binomial Theorem and its Simple Application

119579 In the expansion of \((x-1)(x-2) \ldots(x-18)\), the coefficient of \(x^{17}\) is

1 684
2 -171
3 171
4 -342
WB JEE-2016
Join With Us for More Updates
Binomial Theorem and its Simple Application

119576 The value of \(\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots . .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}\) is

1 \(\frac{2^{51}}{50 !}\)
2 \(\frac{2^{50}}{50 !}\)
3 \(\frac{2^{51}}{51 !}\)
4 \(\frac{2^{50}}{51 !}\)
JEE Main-01.02.2023
Binomial Theorem and its Simple Application

119577 The value of \(\sum_{n=1}^{13}\left(i^n+i^{n+1}\right)\) where \(i=\sqrt{-1}\) equals

1 0
2 i
3 \(-\mathrm{i}\)
4 i-1
AMU-2016
Binomial Theorem and its Simple Application

119578 Let
\(\mathrm{S}=\frac{\mathbf{2}}{\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_0+\frac{\mathbf{2}^2}{\mathbf{2}}{ }^{\mathrm{n}} \mathrm{C}_1+\frac{\mathbf{2}^3}{\mathbf{3}}{ }^{\mathrm{n}} \mathrm{C}_2+\ldots+\frac{\mathbf{2}^{\mathrm{n}+1}}{\mathrm{n}+\mathbf{1}}{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}}\). The n, \(S\) equals

1 \(\frac{2^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
2 \(\frac{3^{\mathrm{n}+1}-1}{\mathrm{n}+1}\)
3 \(\frac{3^{\mathrm{n}}-1}{\mathrm{n}}\)
4 \(\frac{2^n-1}{n}\)
WB JEE-2014
Binomial Theorem and its Simple Application

119579 In the expansion of \((x-1)(x-2) \ldots(x-18)\), the coefficient of \(x^{17}\) is

1 684
2 -171
3 171
4 -342
WB JEE-2016
For More Updates join with Us