Get 2 FREE Instant-Explanations on Filo with code FILOAPP

If { C }_{ 0 },{ C }_{ 1 },{ C }_{ 2 },...,{ C }_{ n } are the

Question

If $C_{0}, C_{1}, C_{2}, ..., C_{n}$ are the coefficients of the expansion of $(1 + x)^{n}$ , then the value of $0 \sum n \frac{C _{k}}{k + 1}$ is

0

\frac{2 ^{n} - 1}{n}

\frac{2 ^{n + 1} - 1}{n + 1}

None of these

Views: 663 students

Found 3 tutors discussing this question

Amelia Discussed

C_{0}, C_{1}, C_{2}, ..., C_{n}

are the coefficients of the expansion of

(1 + x)^{n}

, then the value of

0 \sum n \frac{C _{k}}{k + 1}

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Here

t_{r + 1} = \frac{^{n} C _{r}}{r + 1} = \frac{1}{r + 1} .^{n} C_{r} = \frac{1}{n + 1} .^{n + 1} C_{r + 1}

Putting

r = 0, 1, 2,, ... n

and adding we get,

0 \sum n \frac{^{n} C _{k}}{k + 1} = \frac{1}{n + 1} {^{n + 1} C_{1} +^{n + 1} C_{2} +^{n + 1} C_{3} + ... +^{n + 1} C_{n + 1}}

= \frac{1}{n + 1} {2^{n + 1} -^{n + 1} C_{0}} = \frac{2 ^{n + 1} - 1}{n + 1}

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	If $C_{0}, C_{1}, C_{2}, ..., C_{n}$ are the coefficients of the expansion of $(1 + x)^{n}$ , then the value of $0 \sum n \frac{C _{k}}{k + 1}$ is
Answer Type	Text solution:1
Upvotes	150