StudioLinked – Vocal Runs 2 VSTi, AUi WIN.OSX X86 X64 – Vocal Synthesizer Q: How do you solve $\sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k-1)} = n(n-1)(n-2)$ $$\sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k-1)} = n(n-1)(n-2)$$ I have been able to solve this sum in a piecewise fashion. $\sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k-1)}=\sum_{k=1}^{n-1} \frac{n(n-1)(n-2)}{k(k-1)} + \frac{(n-1)n(n-1)(n-2)}{n(n-1)}=n(n-1)(n-2)+n-1=n(n-1)(n-2)$ However, I have also noticed that when $n=1,2$, the result is $0$ and $1$ respectively. How do you prove that this is the case, and what is the general solution to this sum? A: Rewrite the sum as a telescoping sum: $$ \sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k-1)} = \sum_{k=1}^n (n-k) \frac{n(n-1)(n-2)}{k(k-1)} = \sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k-1)} - \sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k-1)(k+1)} = n(n-1)(n-2) - \sum_{k=1}^n \frac{n(n-1)(n-2)}{k(k+1)}. $$ A: After plugging in $n=1$, the left hand side is .The focus of this project has been to characterize the ER signal regulatory pathway in mammalian cells and the machinery required for its function. Specifically we have identified and characterized several core components of the pathway from yeast to human including the following: 1) the protein kinase ERK1/ERK2, 2) the dual specificity protein phosphatase PP1, 3) the vacuolar protein sorting receptor VPS35 and 4) the mammalian homologue of the yeast VPS36 protein. 1) The ERK1/ERK2 (extracellular signal regulated kinase 1/extracellular signal regulated kinase 2) MAP kinase homologues, we have determined that ERK1/ERK2 is an important component of the ER signal regulatory pathway in mammalian cells and that they are activated by: 1) the Ras-GTPase activating protein (GAP) GAP1 and 2) the protein phosphatase PP1. 2) The dual specificity phosphatase PP1 is a constitutively expressed enzyme which dephosphorylates the activated ERKs and when the MAP kinase pathway is constitutively activated due to over expression of the kinase, ERK activity is reduced. 3) VPS35 is a sorting receptor for the ERK1/ERK2 MAP kinases and appears to be involved in the anterograde transport of activated MAP kinase to the Golgi compartment. 4) The yeast VPS36p protein is a homologue of VPS35 and is required for ERK1p transport out of the endosome compartment into the Golgi. 5) This project has also been successful in identifying several additional ERK activating proteins which includes: 1) the hematopoietic glycoprotein CD59 and 2) the protein tyrosine kinase Lyn. The role of these proteins in the signal regulatory pathway will be determined in order to characterize more precisely the signal transduction pathway.Q: Proving $\ln(\cos^{2x}(x))=2\ln(\cos(x))-x$ by taking the derivative Prove that $$\ln(\cos^{2x}(x))=2\ln(\cos(x))-x.$$ Taking the derivative: $$\ln(\cos^{2x})=2x\cos^{2x-1}+2\ln(\cos(x))$$ What is the next step? 570a42141b
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