The ratio of the sums of the first n even num | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The sum of the first $n$ even numbers is given by the formula $S_{Even} = 2 + 4 + 6 + \dots + 2n = n(n + 1)$.The sum of the first $n$ odd numbers

Vedclass · Accepted Answer

$(n + 1):n$

Vedclass · Answer

(C) The sum of the first $n$ even numbers is given by the formula $S_{Even} = 2 + 4 + 6 + \dots + 2n = n(n + 1)$.The sum of the first $n$ odd numbers is given by the formula $S_{Odd} = 1 + 3 + 5 + \dots + (2n - 1) = n^2$.Therefore,the ratio of the sum of the first $n$ even numbers to the sum of the first $n$ odd numbers is $\frac{S_{Even}}{S_{Odd}} = \frac{n(n + 1)}{n^2} = \frac{n + 1}{n}$.Thus,the ratio is $(n + 1):n$.

The ratio of the sums of the first $n$ even numbers and $n$ odd numbers is

Similar Questions

The sum of the series $(2)^2 + 2(4)^2 + 3(6)^2 + ...$ up to $10$ terms is:

Find the $n^{th}$ term of the series:
$\frac{1}{n} + \frac{n+1}{n} + \frac{2n+1}{n} + \ldots$

If the $10^{\text{th}}$ term of an $A$.$P$. is $\frac{1}{20}$ and its $20^{\text{th}}$ term is $\frac{1}{10}$,then the sum of its first $200$ terms is

The sum of the series $1 + (1 + 2) + (1 + 2 + 3) + \dots$ up to $n$ terms will be:

If $G$ is the geometric mean of $x$ and $y$,then $\frac{1}{G^2 - x^2} + \frac{1}{G^2 - y^2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module