Expand the following binomial- 1- x 2 7

On using the binomial expansion, we get the expression (1+x2)^7=1+^7C_1 x2+ ^7 C_2x^22^2+^7C_3x^32^3+^7C_4x^42^4+^7C_5 x^52^5+^7C_6 x^62^6+^7C_7 x^72^7 We g ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Binomial Expression

Expand the fo...

Question

Expand the following binomial:
${(1 + \frac{x}{2})}^{7}$

Open in App

Solution

On using the binomial expansion, we get the expression
${(1 + \frac{x}{2})}^{7} = 1 +^{7} C_{1} \frac{x}{2} +^{7} C_{2} \frac{x^{2}}{2^{2}} +^{7} C_{3} \frac{x^{3}}{2^{3}} +^{7} C_{4} \frac{x^{4}}{2^{4}} +^{7} C_{5} \frac{x^{5}}{2^{5}} +^{7} C_{6} \frac{x^{6}}{2^{6}} +^{7} C_{7} \frac{x^{7}}{2^{7}}$

We get
$\Rightarrow 1 + \frac{7 x}{2} + \frac{21 x^{2}}{4} + \frac{35 x^{3}}{8} + \frac{35 x^{4}}{16} + \frac{21 x^{5}}{32} + \frac{7 x^{6}}{64} + \frac{x^{7}}{128}$

Suggest Corrections

Expand the following binomial:(1+x2)7

On using the binomial expansion, we get the expression(1+x2)7=1+7C1x2+7C2x222+7C3x323+7C4x424+7C5x525+7C6x626+7C7x727We get⇒1+7x2+21x24+35x38+35x416+21x532+7x664+x7128

Expand the following binomial:
${(1 + \frac{x}{2})}^{7}$