Question

2. The ratio of the sum of first n even natural numbers and the sum of first n odd
natural numbers is-
​

Answer 1

Answer:

3:2

Step-by-step explanation:

let n be 2

sum of first 2 even numbers is 2+4=6

sum of first 2 odd numbers is 1+3=4

ratio - 6:4= 3:2

Answer 2

Answer:

Let the first n odd numbers represent the A.P: 1,3,5,7,9....

and the first n even numbers represent the A.P' : 2,4,6,8,10....

Now, for the 1st A.P,

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

Sn = n/2 (2(1)+(n-1)2)

Sn = n/2 (2+2n-2)

Sn = (n/2)(2n)

Sn = n^2 ........ (i)

Now, for the 2nd A.P',

Sn' = n/2 (2a' +(n-1)d')

Sn' = n/2 (2(2) +(n-1)2)

Sn' = n/2 (4 + 2n - 2)

Sn' = n/2 (2n + 2)

Sn' = n/2 (2 (n+1))

Sn' = n (n+1) = n^2 + n ...... (ii)

Now, dividing (ii) by (i),

Sn'/Sn = (n^2 + n)/n^2

= [n(n+1)]/n^2

= (n + 1)/n

Therefore, ratio = n + 1 : n