Number of terms in the binomial expansion of (x+a)⁵³+(x-a)⁵³ is

Step-by-step solution

The expansion of (x+a)^ n + (x-a)^ n is given by 2[^ n C₀x^ n + ^ n C₂x^ n-2 a² + ^ n C₄x^ n-4 a⁴ + ] . For n = 53 , the expansion is (x+a)⁵³ + (x-a)⁵³ = 2[⁵³C₀x⁵³ + ⁵³C₂x⁵¹a² + + ⁵³C₅₂x¹a⁵²] . The terms in the expansion correspond to the values of k in ⁵³C_ 2k x^ 53-2k a^ 2k where 2k ranges from 0 to 52 . The possible values for k are 0, 1, 2, , 26 . The total number of terms is the number of values in the set 0, 1, 2, , 26 , which is 26 - 0 + 1 = 27 . Answer: 27