Question

If the sum of first n even natural number is equal to k times the sum of first n odd number then find k

Answer 1

Answer:

Here's the answer : (1+n)/n

Step-by-step explanation:

first even natural number is : 2

first odd natural number is : 1

sum of n even natural numbers = n/2{2*2 +d(n-1)}

sum of n odd natural numbers =  n/2{2*1 +d(n-1)}

ATP,

n/2{2*2 +d(n-1)} = k * n/2{2*1 +d(n-1)}

so, k = n/2{2*2 +d(n-1)} / n/2{2*1 +d(n-1)}

     k = 4 + d(n-1) / 2 + d(n-1)

here, d = 2 (as, the difference between 2 consecutive odd or, even number is 2)

so, k = 4 + 2(n-1) / 2 + 2(n-1)

        = 2 + n -1 / 1 + n -1

        = (1 + n)/ n