Question

Find the sum of all coefficients in the following binomial expansion.
a. (2u + v)^10
b. (2u − v)^10
c. (2u − 3v)^11
d. (u − 3v)^11
e. (1 + i)^10
f. (1 − i)^10
g. (1 + i)^200
h. (1 + i)^201

Answer 1

Answer:

We can find the sum of all the coefficients by substituting all the variables in the expansion with one.

a. u=1,v=1

sum=$(2*1+1)^{10}$=$3^{10}$

b.u=1,v=1

sum=$(2*1-1)^{10}$=1

c.u=1,v=1

sum=$(2*1-3*1)^{11$=-1

d.u=1,v=1

sum=$(1-3*1)^{11}$=-$2^{11$

e.i=1

sum=$(1+1)^{10$=$2^{10$

f.i=1

sum=$(1-1)^{10$=0

g.i=1

sum=$(1+1)^{200$=$2^{200$

h.i=1

sum=$(1+1)^{201}$=$2^{201$