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)+…+(1+2+…,+n)/(1^3+2^3+…n^3) . If 100 S_n=n, then n is equal to:

MARKS Content Team · Accepted Answer

Correct answer: (B) 199. Given, S_n=(11^3+1+21^3+2^3+1+2+31^3+2^3+3^3+…+1+2+…+n1^3+2^3+…+n^3T_n=nn+12nn+12^2T_n=2)/(nn+1)=21/n-1/(n+1) S_n=2∑n=1n1/n-1/(n+1) S_n=21-1/(n+1)=2n/(n+1) Given, 100S_n=n⇒100×2n/(n+1)=n n+1=200 n=199

Let $S_{n} = \frac{1}{1^{3}} + \frac{1 + 2}{1^{3} + 2^{3}} + \frac{1 + 2 + 3}{1^{3} + 2^{3} + 3^{3}} + \dots + \frac{1 + 2 + \dots, + n}{1^{3} + 2^{3} + \dots n^{3}}$ . If $100 S_{n} = n,$ then $n$ is equal to:

Solution

Relevant Questions

Let Sn=113+1+213+23+1+2+313+23+33+…+1+2+…,+n13+23+…n3 . If 100 Sn=n, then n is equal to:

Solution

Relevant Questions

Let $S_{n} = \frac{1}{1^{3}} + \frac{1 + 2}{1^{3} + 2^{3}} + \frac{1 + 2 + 3}{1^{3} + 2^{3} + 3^{3}} + \dots + \frac{1 + 2 + \dots, + n}{1^{3} + 2^{3} + \dots n^{3}}$ . If $100 S_{n} = n,$ then $n$ is equal to: