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 ? Share with your friends Share 5 Varun Rawat answered this 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. 9 View Full Answer Shivam Kumar answered this 45 -4