Let C r n denote the binomial coefficient of x r in the expansion of ( 1 + x ) n . If ∑ k = 0 10 2 2 + 3 k C k n = α . 3 10 + β · 2 10 , α , β ∈ R , then α + β is equal to ___ .

Question

Let C r n denote the binomial coefficient of x r in the expansion of ( 1 + x ) n . If &#8721; k = 0 10 2 2 + 3 k C k n = &#945; . 3 10 + &#946; &#183; 2 10 , &#945; , &#946; &#8712; R , then &#945; + &#946; is equal to ___ .

Quantrex Academy · Accepted Answer

Correct answer: 0

Instead of C k n it must be C k 10 i.e. &#8721; k = 0 10 2 2 + 3 k C k 10 = &#945; &#183; 3 10 + &#946; &#183; 2 10 L H S = 4 &#8721; k = 0 10 C k 10 + 3 &#8721; k = 0 10 k &#183; 10 k &#183; C k - 1 9 = 4 . 2 10 + 3 . 10 . 2 9 = 19 . 2 10 = &#945; . 3 10 + &#946; . 2 10 &#8658; &#945; = 0 , &#946; = 19 &#8658; &#945; + &#946; = 19

Let C r n denote the binomial coefficient of x r in the expansion of ( 1 + x ) n . If ∑ k = 0 10 2 2 + 3 k C k n = α . 3 10 + β · 2 10 , α , β ∈ R , then α + β is equal to ___ .

Correct answer

Step-by-step solution

More from Binomial Theorem

Let C r n denote the binomial coefficient of x r in the expansion of ( 1 + x ) n . If &#8721; k = 0 10 2 2 + 3 k C k n = &#945; . 3 10 + &#946; &#183; 2 10 , &#945; , &#946; &#8712; R , then &#945; + &#946; is equal to ___ .

Correct answer

Step-by-step solution

More from Binomial Theorem

Let C r n denote the binomial coefficient of x r in the expansion of ( 1 + x ) n . If ∑ k = 0 10 2 2 + 3 k C k n = α . 3 10 + β · 2 10 , α , β ∈ R , then α + β is equal to ___ .