Q What is the sum of the binomial coefficients in the expansion of 1+x50 Q What is - Maths - Binomial Theorem

Question

Q What is the sum of the binomial coefficients in the expansion of
1 + x 50 ?
Q What is the sum of the coefficients of odd powers of x in the
expansion of 1 + x 50 ?

Varun Rawat · Accepted Answer

1 1 + x50 = C050   150 
 x0 + C150   149 
 x1 + C250   148 
 x2 +  +C5050   10 
 x50  Putting x = 1, we get      1+150 = C050 + C150  + C250 + 
+C5050 ⇒ C050 + C150  + C250 + 
+C5050 = 250So, sum of binomial coefficients in the expansion of 1+x50 is 250
2 1 + x50 = C050   150 
 x0 + C150   149 
 x1 + C250   148 
 x2 +  +C5050   10 
 x50  Putting x = -1, we get1-150 = C050 - C150  + C250 - C350 +
+C5050 ⇒0 = C050 + C250 + C450 + 
 - C150 + C350 + C550 + 
⇒C050 + C250 + C450 + 
 +C5050 = C150 + C350 + C550 + 
+C4950                  
1⇒sum of  coefficients of even terms in the expansion of 1+x50 = sum of  coefficients of odd terms in the expansion of 1+x50⇒C050 + C150  + C250 + 
+C5050 = 2C150 + C350 + C550 + 
+C4950⇒C150 + C350 + C550 + 
+C4950 = 2502 = 249⇒sum of  coefficients of odd terms in the expansion of 1+x50 is 249

Q. What is the sum of the binomial coefficients in the expansion of 1 + x 50 ? Q. What is the sum of the coefficients of odd powers of x in the expansion of 1 + x 50 ?

Q. What is the sum of the binomial coefficients in the expansion of ${(1 + x)}^{50}$ ?
Q. What is the sum of the coefficients of odd powers of x in the expansion of ${(1 + x)}^{50}$ ?