Sumatoria

Algebra Level 3

How much is it when n=2015


The answer is 0.999999754.

Luis Lopez by Luis Lopez , 23, Colombia

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2 solutions

Shaurya Gupta
Nov 13, 2015

2 k + 1 k 4 + 2 k 3 + k 2 = ( k + 1 ) 2 − k 2 k 2 ( k + 1 ) 2 = 1 ( k ) 2 − 1 ( k + 1 ) 2 \displaystyle \frac { 2k+1 }{ k^{ 4 }+2k^{ 3 }+k^{ 2 } } \quad =\quad \frac { (k+1)^{ 2 }-k^{ 2 } }{ k^{ 2 }(k+1)^{ 2 } } \quad =\quad \frac { 1 }{ (k)^2 } -\frac { 1 }{ (k+1)^2 }

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Luis Lopez
Nov 12, 2015

I'm from Colombia... por eso está en español

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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