Let S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + … + 1 + 2 + … , + n 1 3 + 2 3 + … n 3 . If 100   S n = n , then n is equal to:

Question

Let S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + &#8230; + 1 + 2 + &#8230; , + n 1 3 + 2 3 + &#8230; n 3 . If 100 &#160; S n = n , then n is equal to:

Aicharya · Accepted Answer

Given, S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + &#8230; + 1 + 2 + &#8230; + n 1 3 + 2 3 + &#8230; + n 3 T n = n n + 1 2 n n + 1 2 2 T n = 2 n n + 1 = 2 1 n - 1 n + 1 S n = 2 &#8721; n = 1 n 1 n - 1 n + 1 S n = 2 1 - 1 n + 1 = 2 n n + 1 Given, 100 S n = n &#8658; 100 &#215; 2 n n + 1 = n n + 1 = 200 n = 199

Let S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + … + 1 + 2 + … , + n 1 3 + 2 3 +…

Solution

Let S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + &#8230; + 1 + 2 + &#8230; , + n 1 3 + 2 3 +…

Solution

Let S n = 1 1 3 + 1 + 2 1 3 + 2 3 + 1 + 2 + 3 1 3 + 2 3 + 3 3 + … + 1 + 2 + … , + n 1 3 + 2 3 +…