Confusing Sum

Algebra Level 4

∑ n = 1 ∞ n 1 + n 2 + n 4 = ? \Large \sum_{n=1}^{\infty} \frac{n}{1+n^2+n^4}= \ ? \


The answer is 0.5.

Rishi Raj by Rishi Raj , 23, India

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2 solutions

Rishabh Jain
Feb 16, 2016

Summation can be written as : ∑ n = 1 ∞ n ( n 2 + 1 − n ) ( n 2 + 1 + n ) \large\displaystyle\sum_{n=1}^{\infty}\dfrac{n}{(n^2+1-n)(n^2+1+n)} = 1 2 ( ∑ n = 1 ∞ 1 ( n 2 + 1 − n ) − 1 ( n 2 + 1 + n ) ) \large=\dfrac{1}{2}(\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{(n^2+1-n)} - \dfrac{1}{(n^2+1+n)}) ( A telescopic series ) (\color{#007fff}{\text{A telescopic series}}) = 1 2 ( 1 ) = 0.5 \large =\dfrac{1}{2}(1)=\huge\color{#D61F06}{\boxed{\color{forestgreen}{0.5}}}

13 Helpful 0 Interesting 0 Brilliant 0 Confused

I have use the same method.

Niranjan Khanderia - 5 years, 3 months ago

I HAVE seen 5-6 questions same on this site

Kaustubh Miglani - 5 years, 3 months ago
Andromeda Stark
Apr 27, 2021

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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