How do I calculate this sum in terms of 'n'? I know this is a harmonic progression, but I can't find how to calculate the summation of it. Also, is it an expansion of any mathematical function? 1 ...

Oct 29, 2016 · I know that the sum of powers of $2$ is $2^{n+1}-1$, and I know the mathematical induction proof. But does anyone know how $2^{n+1}-1$ comes up in the first place. For …

Mar 30, 2015 · Explore related questions elementary-number-theory summation fibonacci-numbers See similar questions with these tags.

But is it possible to express the summation definition of $e^x$, without using them ? Since, I am regenerating my math knowledge I want to go step by step to calculus, differential equations …

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I've been trying to figure out the intuition behind the closed formula: $$\\sum_{i=1}^n i^{2} = \\frac{(n)(n+1)(2n+1)}{6}$$ This is not hard to prove via induction, so I'm not interested in the …

Explore related questions elementary-number-theory summation See similar questions with these tags.

Sep 2, 2017 · $\\sum_{i=1}^n i$ is the same as $\\frac{n(n+1)}{2}$. Can someone explain how the sigma notation is converted to this? I'm trying to figure out if there's a way to convert …

Mar 3, 2018 · 13 $\displaystyle\sum_ {i,t}$ means the same as $\displaystyle\sum_i \sum_t$. In the second notation, a specific summation order is given, whereas in the first one there isn't. …

$ \\sum_{i=0}^{5}{i^2} = 0^2+1^2+2^2+3^2+4^2+5^2 = 55 $ How to write this Sigma notation only for odd numbers: $ 1^2+3^2+5^2 = 35 $ ?