Algebra Answers

Let xi ∈ R such that 0 < x1 ≤ x2 ≤ .....≤ xn,
n ≥ 2, and
1/(1+x1) + 1/(1+x2) +........+1/(1+xn) =1 then show that
√x1 + √x2 +........+ √xn ≥ (n-1) {1/√x1 + .....+ 1/√xn}

Show using laws and theorems of inequality

Show that
1 + 1/√2+. . . +1/√n ≥ √[2(n − 1)] for n∈ N, n> 1
Solve using laws and theorem of inequalities

Show that
1 + 1/√2+. . . +1/√n ≥ √{2(n − 1)} for n∈ N, n> 1.

Find the geometric series of a geometric sequence if the nth term is 20, the number of terms is 10 and the common ration is 2

Show that
1 + 1/√2+. . . +1/√n ≥ √{2(n − 1)} for n∈ N, n> 1
Solve using inequalities

Let x belongs to R such that 0≤ x1 ≤ x2 ≤ ...... ≤ xn, n≥2 and 1/(1+x1) + 1/(1+x2) + ......+1/(1+xn)=1 then show that √x1+√x2+...+√xn ≥ (n-1)(1/√x1 + ......+ 1/√xn)
Solve using inequalities

Write an odd natural number as a sum of two integers m1 and m2 in a way that m1m2 is maximum. Solve using inequalities

5+55+555.....to n terms

$$C=5/9(F-32)$$

The equation above shows how temperature $F$, measured in degrees Fahrenheit, relates to a temperature $C$, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $5/9$ degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of $5/9$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only
B) II only
C) III only
D) I and II only

A={√2, IGNOU, algebra} is a set.
Is it true or false? Justify your answer