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

Maths for fun-mathematics- in our lives, Maths For Fun :  Often, when I ha...

Maths For Fun :  Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and

Find the exact points and factorise , Consider the function f(x) = x 2 - 2...

Consider the function f(x) = x 2 - 2x - 1. (a) Factorise f(x) exactly. (b) Find the exact points (x and y coordinates required) where the graph of y = f(x) cuts the x and y-

Factors, Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its on...

Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its only factors. Sketch the graph of f. State all the zeros of f.

Surds and logarithms, what are these all about and could i have some exampl...

what are these all about and could i have some examples of them please

Surface area, Find the amount of sheet metal need to form a conical funnel ...

Find the amount of sheet metal need to form a conical funnel of base radius 30cm with a vertical height of 50cm, allowing for 0.5cm overlap. Find the total surface area?

Probability, A man enter a lucky draw that requires him to pick five differ...

A man enter a lucky draw that requires him to pick five different integers from 1 through 30 inclusive .he chooses his five number in such a way that the sum of their log base 10 i

Limit properties, Limit Properties :  The time has almost come for us t...

Limit Properties :  The time has almost come for us to in fact compute some limits.  Though, before we do that we will require some properties of limits which will make our lif

Lines- common polar coordinate graphs, Lines- Common Polar Coordinate Graph...

Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1.  θ = β We are able to see that this is a line by converting to Car

Homework, How do you simplify 10:30:45

How do you simplify 10:30:45

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