Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + … + 10 10 C 10 2 , where 10 C r ,   r ∈ 1,2 , … . , 10 denote binomial coefficients. Then, the value of 1 1430 X is ______ .

Question

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + &#8230; + 10 10 C 10 2 , where 10 C r , &#160; r &#8712; 1,2 , &#8230; . , 10 denote binomial coefficients. Then, the value of 1 1430 X is ______ .

Aicharya · Accepted Answer

X = ∑ r = 0 n r . n C r 2 ; n = 10 X = n . ∑ r = 0 n n C r . n - 1 C r - 1 X = n . ∑ r = 1 n n C n - r . n - 1 C r - 1 X = n . 2 n - 1 C n - 1 ; n = 10 X = 10 . 19 C 9 X 1430 = 1 143 . 19 C 9 = 646

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + … + 10 10 C 10 2 , where 10 C r ,   r ∈ 1,2 ,…

Solution

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + &#8230; + 10 10 C 10 2 , where 10 C r , &#160; r &#8712; 1,2 ,…

Solution

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + … + 10 10 C 10 2 , where 10 C r , r ∈ 1,2 ,…