Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 177146 by mathlove last updated on 01/Oct/22

$$f\left(x\right)=f(x-1)+x^2+2x$$$$f\left(6\right)=33faindvolueoff\left(50\right)=?$$

Answered by cortano1 last updated on 01/Oct/22

$$\mathrm{f}\left(\mathrm{x}\right)-\mathrm{f}(\mathrm{x}-1)={\mathrm{x}}^2+2\mathrm{x}$$$$\underset{\mathrm{x}=7}{\sum ^{50}}\mathrm{f}\left(\mathrm{x}\right)-\mathrm{f}(\mathrm{x}-1)=\underset{\mathrm{x}=7}{\sum ^{50}}({\mathrm{x}}^2+2\mathrm{x})$$$$\mathrm{f}\left(50\right)-\mathrm{f}\left(6\right)=\underset{\mathrm{x}=7}{\sum ^{50}}({\mathrm{x}}^2+2\mathrm{x})$$

Answered by mr W last updated on 01/Oct/22

$$f\left(x\right)-f(x-1)=x^2+2x$$$$a_n-a_{n-1}=n^2+2n$$$$\underset{n=1}{\sum ^n}(a_n-a_{n-1})=\underset{n=1}{\sum ^n}(n^2+2n)$$$$a_n-a_0=\frac{n(n+1)(2n+1)}{6}+n(n+1)$$$$\Rightarrow a_n=a_0+\frac{n(n+1)(2n+7)}{6}$$$$\Rightarrow a_6=a_0+\frac{6\times 7\times 19}{6}=33\Rightarrow a_0=-100$$$$\Rightarrow a_n=\frac{n(n+1)(2n+7)}{6}-100$$$$\Rightarrow f\left(x\right)=\frac{x(x+1)(2x+7)}{6}-100$$$$\Rightarrow f\left(50\right)=\frac{50\times 51\times 107}{6}-100=45375$$

Commented by mathlove last updated on 02/Oct/22

$$thanksmr$$

Commented by Tawa11 last updated on 02/Oct/22

$$\mathrm{Great}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com