Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$ - Mathematics...
I managed to show that the series converges but I was unable to find the sum. Any help/hint will go a long way. Using an integral form of the Beta function the summation becomes S=∞∑n=11n(n+1)(n+2)=12∫10(∞∑n=1xn−1)(1−x)2dx=12∫10(1−x)21−xdx=12∫10(1−x)dx=14.
formula - What is the proof of of... - Stack Overflow
Harmonic series (mathematics) - Wikipedia
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions One way to prove divergence is to compare the harmonic series with another divergent series, where each denominator is replaced with the next-largest power of two
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Auxiliary Space: O(1) Method 2: In this case we use formula to add sum of series. We can avoid this overflow to some extent using the fact that n*(n+1) must be divisible by 2 and (n+2)*(n+3) is also divisible by 2.
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