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

Find out a particular solution to equation, Example: Find out a particular...

Example: Find out a particular solution to y'' - 4y' - 12 y = 3e 5t Solution The point here is to get a particular solution, though the first thing that we're going to

Rational Number Application, in the horizontal bar event the u.s.a scored 2...

in the horizontal bar event the u.s.a scored 28.636,gremany scroed 28.7,romnia scored 27.962,and chain scored 28.537 points.which list shows these scored in descending order

How to find total no. of unordered pairs , How to find total no. of unorder...

How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into

Time series models, Time Series Models Additive Model Time seri...

Time Series Models Additive Model Time series value = T +S +C +R Whereas S, C and R are expressed in absolute value Additive Model model is best suited where the

Evaluating functions, Next we have to talk about evaluating functions.  Eva...

Next we have to talk about evaluating functions.  Evaluating a function is in fact nothing more than asking what its value is for particular values of x. Another way of looking at

Show that p ( x ) = 2 x3 - 5x2 -10 x + 5 intermediate value , Example   Sh...

Example   Show that p ( x ) = 2 x 3 - 5x 2 -10 x + 5 has a root somewhere in the interval [-1,2]. Solution What we're actually asking here is whether or not the function wi

what is probability that point will be chosen from triagle, In the adjoini...

In the adjoining figure ABCD is a square with sides of length 6 units points P & Q are the mid points of the sides BC & CD respectively. If a point is selected at random from the i

Example of normal distribution, The mathematics results of 20 first-year un...

The mathematics results of 20 first-year university students are given, together with their results of their performances in the year 12 semester Test and Final Assignment:

Numercial analysis and computer techniques, write FORTRAN programme to gene...

write FORTRAN programme to generate prime numbers between 1 and 100

Precalculus, Find the standard form of the equation of the parabola with a ...

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

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