Prove that the ratio of the sum of odd terms, Mathematics

Assignment Help:

If there are (2n+1)terms  in an AP ,prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n

Ans:    Let a, d be the I term & Cd of the AP.

∴ ak = a + (k - 1) d

s1 = sum to odd terms

s1 = a1 +  a3 + ......... a 2n + 1

s1  = n +1/2 [a1 + a2 n +1 ]

= n + 1/2 [2a1 + 2nd]

s1 = (n + 1) (a + nd)

s2 = sum to even terms

s2 = a2 + a4 + ..... a 2n

s2  = n/2 [a2 + a2n  ]

= n/2 [a + d + a + (2n - 1)d]

=n [a + nd]

∴ s1 : s2 = (n +1)(a nd )/n(a nd )

= n+1/n


Related Discussions:- Prove that the ratio of the sum of odd terms

What is probability that a person selected at random eyes, If 65% of the po...

If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro

Find the discount factors and linear interpolation, Question: All rates...

Question: All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765), and the bond prices to 3 decimal place

Find out the value of the subsequent summation, Using the formulas and prop...

Using the formulas and properties from above find out the value of the subsequent summation. c The first thing that we require to do here is square out the stuff being summe

Math 100, introduction to decimals

introduction to decimals

Caselets, how are indian customers visiting shoppers stop any different fro...

how are indian customers visiting shoppers stop any different from customers of developed western countries

Algebra function., problem to understand an problem; f(X-2)=X+3 / X-4

problem to understand an problem; f(X-2)=X+3 / X-4

SIMPLE INTEREST, A payday loan company charges a $95 fee for a $500 payday ...

A payday loan company charges a $95 fee for a $500 payday loan that will be repaid in 11 days. Treating the fee as interest paid, what is the equivalent annual interest rate?

Combined mean and standard deviation -illustration, Combined mean Assu...

Combined mean Assume m be the combined mean Assume x 1 be the mean of first sample Assume x 2 be the mean of the second sample Assume n 1 be the size of the 1 st

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd