Question

If the sum of first 20 even natural numbers is equal to k times the sum of first 20 odd natural numbers,

then k is equal to​

Answer 1

Hope this will help you......

Answer 2

Answer:

If the sum of first 20 even natural numbers is equal to k times the sum of first 20 odd natural numbers, then the value of k = 21/20

Step-by-step explanation:

Given :

The sum of first 20 even natural numbers  =  k times the sum of first 20 odd natural numbers

To Find :

The value of k

Solution :

Since we are given that the sum of first 20 even natural numbers  =  k times the sum of first 20 odd natural numbers

since we know that the sum of first n natural even numbers = n ( n + 1 )

Hence the sum of first 20 even natural numbers = 20 ( 20 + 1 ) = 20 x 21 = 420

And the sum of first n natural odd numbers = $n^2$

Hence the sum of first 20 odd natural numbers = 20^2 = 400

Since we are given that the sum of first 20 even natural numbers  =  k times the sum of first 20 odd natural numbers

so,

420 = k x 400

k = 420/400 = 42/40

k = 21/20

Therefore we have calculated that the value of k = 21/20

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