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

Examples of linear equation, Examples of Linear Equation Please provid...

Examples of Linear Equation Please provide me some Examples of Linear Equation?

Differentiation of a formula with two variables, I would like to calculate ...

I would like to calculate the high point of a mathematical formula with two unknown variables. At the same time I made the 1st derivation of the function. How can I best program th

Find final position of point by rotation -translation matric, Question: ...

Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po

The index of industrial production, The index of industrial production ...

The index of industrial production This is a quantity index compiled by the government. This measures changes in the volume of production in main industries. The index is a ex

#title, how do you do hard math!!!

how do you do hard math!!!

Solve 6 sin ( x/2)= 1 on [-20, Solve 6 sin ( x/2)= 1 on [-20,30] Soluti...

Solve 6 sin ( x/2)= 1 on [-20,30] Solution Let's first work out calculator of the way since that isn't where the difference comes into play. sin( x/2)= 1/6   ⇒x/2= sin

Calculus (The squeeze theorem), When finding the limit as x approaches 0 th...

When finding the limit as x approaches 0 the for function (square root of x^3 + x^2) cos(pi/2x) would the limit not exist because there would be a zero in the denominator?

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