$(1+x{)}^{n}\ge 1+nx$, for x> -1

Lisa Hardin
2022-07-25
Answered

Show by induction that :

$(1+x{)}^{n}\ge 1+nx$, for x> -1

$(1+x{)}^{n}\ge 1+nx$, for x> -1

You can still ask an expert for help

asked 2022-08-04

Write the quadratic function in standard form. $f(x)={x}^{2}+32x+256$

asked 2022-08-04

$1.{x}^{2}-25/5-X2.{x}^{2}-7x+6/{x}^{2}+11x+103.{x}^{-9}/{x}^{3}+{x}^{2}-9x-9$ (2nd part) Perform mulitplication or devision and simplyfy $1.{x}^{2}-36/x$ divided by ${x}^{3}-6{x}^{2}/{x}^{2}+x$ (3rd part) perform adition or subtraction and simplyfy $1.3/x-1-52.2/{x}^{2}-x-2+10/{x}^{2}+2x-8$ (last part) simplyfy the complex fraction 1. (x under square rootx- 1/2 x x under square root sign/x under square rootsign.

asked 2022-03-18

Comparing 2 infinite continued fractions

$A=1+d\frac{1}{1+\frac{1}{1+\frac{1}{\ddots}}}$

$B=2+d\frac{1}{2+\frac{1}{2+\frac{1}{\ddots}}}$

Given the two infinite continued fractions A and B above, which is larger, 2A or B?

asked 2022-04-26

Solve the given system of quadratic equations

${x}^{2}+xy+xz=2$

${y}^{2}+yz+xy=3$

${z}^{2}+zx+yz=4$

asked 2022-03-14

What would be the range for the function

$f\left(x\right)={\mathrm{log}}_{3}(5+4x-{x}^{2})$

asked 2022-07-29

Find the solution of the given initial value problem.

${y}^{\prime}+(2/t)y=(\mathrm{cos}t){t}^{2},y(3.14)=0,t>0$

${y}^{\prime}+(2/t)y=(\mathrm{cos}t){t}^{2},y(3.14)=0,t>0$

asked 2022-03-28

Consider the polynomial $f\left(x\right)={x}^{2}-5mx+10m-4$ , find m such that there exist a number a that satisfies $f\left(a\right)=f\left(2a\right)=0$ .