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 ...

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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 …

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Mar 8, 2015 · Your induction hypothesis and what you are trying to prove for induction are both incorrect. What you are trying to prove is that the sum of the powers of 2 2 up to n n is equal to …

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Feb 23, 2021 · I am trying to help a high school student to solve summation calculation problems. The i i value of most answers I found was based on i = 1 i = 1 like this: Now, the i i value of our …

The first chapter of Concrete Mathematics by Graham, Knuth, and Patashnik presents about seven different techniques for deriving this identity, so you might be interested to look at that.

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Jun 30, 2016 · I search a general rule for calculating the logarithm of a sum or addition. I know that $$\ln { (a+b)}=\ln {\left (a\left (1+\frac b a\right)\right)}=\ln { (a)}+\ln ...