If S=a1+a2+……+an,ai∈R+ for i=1 to n, then prove that S−a1S+S−a2S+……+S−anS≥n−1n2,∀n≥2

Click here to view the solution.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

If {S}={a}_{{1}}+{a}_{{2}}++{a}_{{n}},{a}_{{i}}{R}^{+} for i=1

Question

If $S = a_{1} + a_{2} + \dots\dots + a_{n}, a_{i} \in R^{+}$ for i=1 to n, then prove that $\frac{S}{S - a _{1}} + \frac{S}{S - a _{2}} + \dots\dots + \frac{S}{S - a _{n}} \geq \frac{n ^{2}}{n - 1}, \forall n \geq 2$

Views: 739 students

Found 7 tutors discussing this question

Noah Discussed

S = a_{1} + a_{2} + \dots\dots + a_{n}, a_{i} \in R^{+}

for i=1 to n, then prove that

\frac{S}{S - a _{1}} + \frac{S}{S - a _{2}} + \dots\dots + \frac{S}{S - a _{n}} \geq \frac{n ^{2}}{n - 1}, \forall n \geq 2

9 mins ago

Discuss this question LIVE

9 mins ago

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

S = a_{1} + a_{2} + \dots\dots + a_{n}, a_{i} \in R^{+}

for i=1 to n, then prove that

\frac{S}{S - a _{1}} + \frac{S}{S - a _{2}} + \dots\dots + \frac{S}{S - a _{n}} \geq \frac{n ^{2}}{n - 1}, \forall n \geq 2