Using binomial theorem determine which number is smaller (1.2)400… - Vidyadip

Question

Using binomial theorem determine which number is smaller (1.2)⁴⁰⁰⁰ or 800?

✓

Answer

$(1.2)^{4000}=(1+0.2)^{4000}$

$={^{4000}\text{C}}_0(0.2)^0(1)^{4000}+{^{4000}\text{C}}_1(0.2)^1{1}^{3999}+....\\+{^{4000}\text{C}}_400(0.2)^0(1)^{4000}(0.2)^{4000}1^0$

$=1 + 4000 \times 0.2 \times 1 +.......+(0.2)^{4000}$

$= 1 + 800 +.......+(0.2)^{4000}$

Here, we dearty observe (1, 2)⁴⁰⁰⁰ is less than (801) thus, (1, 2)⁴⁰⁰⁰ < 800.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Binomial Theorem→Binomial Theorem — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the equation to the ellipse in the following case:

Length of major axis 26, foci $(\pm5, 0)$

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{x^2}{100}+\frac{y^2}{400}=1$

Prove the following by the principle of mathematical induction:
$\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{(\text{3n-1)(3n+2)}}=\frac{\text{n}}{\text{6n}+4}$

If $\Big(\frac{1+\text{i}}{1-\text{i}}\Big)^3-\Big(\frac{1-\text{i}}{1+\text{i}}\Big)^3=\text{x}+\text{iy,}$ find (x, y)

Represent to solution set of each of the following inequations graphically in two dimensional plane:
$\text{y}>2\text{x}-8$

Sketch the graphs of the following functions:
$\text{f(x)}=2\text{cosec }\pi\text{x}$

If $\text{z}_1=2-\text{i}, \ \text{z}_2=-2+\text{i},$ Find
$\text{Re}\Big(\frac{\text{z}_1\text{z}_2}{\text{z}_1}\Big)$

In a circle of diameter 40cm, the length of a chord is 20cm. Find the length of minor arc of the chord.

Show that $\frac { 1 \times 2 ^ { 2 } + 2 \times 3 ^ { 2 } + \ldots \ldots + n \times ( n + 1 ) ^ { 2 } } { 1 ^ { 2 } \times 2 + 2 ^ { 2 } \times 3 + \ldots \ldots + n ^ { 2 } ( n + 1 ) } = \frac { 3 n + 5 } { 3 n + 1 }$

Find the rational number having the following decimal expansions:

$0.\overline{68}$