Saved Bookmarks
| 1. |
What is the sum of all the coefficients in the expansion of (1 + x)n ?1. 2n2. 2n - 13. 2n - 14. 2(n - 1) |
|
Answer» Correct Answer - Option 1 : 2n Concept: (1 + x)n = nC0 + nC1 x + nC2 x2 +...+ nCn xn Calculations: We know that (1 + x)n = nC0 + nC1 x + nC2 x2 +...+ nCn xn To find the sum of all the coefficients in the expansion of (1 + x)n , put x = 1 ⇒(1 + 1)n = nC0 + nC1 1 + nC2 12 +...+ nCn 1n ⇒(2)n = nC0 + nC1 + nC2 +...+ nCn ⇒ nC0 + nC1 + nC2 +...+ nCn= 2n Hence, the sum of all the coefficients in the expansion of (1 + x)n = 2n |
|