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summation - The idea behind the sum of powers of 2 - Mathematics Stack . . .
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 example, sum of n numbers is
Finding the infinite sum of $e^{-n}$ using integrals
calculus real-analysis sequences-and-series analysis summation See similar questions with these tags
summation - Sum of Fibonacci numbers - Mathematics Stack Exchange
elementary-number-theory summation fibonacci-numbers See similar questions with these tags
summation - How to convert Sigma Notation to a regular formula . . .
$\\sum_{i=1}^n i$ 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 $\\sum_{i=1}^n i+(x-1)$
summation - How to prove a formula for the sum of powers of $2$ by . . .
How do I prove this by induction? Prove that for every natural number n, $ 2^0 + 2^1 + + 2^n = 2^{n+1}-1$ Here is my attempt Base Case: let $ n = 0$ Then, $2^{0+1} - 1 = 1$ Which is true
summation - Sum of odd numbers always gives a perfect square . . .
Explore related questions elementary-number-theory summation See similar questions with these tags
summation - Is ∑ with negative value solvable? - Mathematics Stack Exchange
Sigma notation is shorthand for iterated addition The expression following the Sigma is the addend, and the operator for each iteration is addition As addition is commutative, it matters not the positive or negative direction of the iteration One can go from some initial index to a negative number What may be forgotten in the notation is that there is an assumed increment One may consider
summation - How do you compute the sum of k * a^k - Mathematics Stack . . .
We have the sum $$\\sum_{k=0}^{n} a^k k,$$ where a is a constant and we need the answer in terms of $n$ How can we go about solving this? If $a$ were a variable we