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Grade: 11

                        

20 ∑ r. ( 20 Cr) 2 = ? r=0 Please Give Full explanation

5 months ago

Answers : (1)

Aditya Gupta
2056 Points
							
note that we have the following property of summation: ∑r=m to n f(r) = ∑r=m to n f(m+n – r)
so, let S= ∑ r. (20Cr).....(1)
using property S= ∑ (0+20 – r). (20C(0+20 – r))
but nCr= nC(n-r)
so, S= ∑ (20 – r). (20Cr).........(2)
add (1) and (2)
2S= ∑ 20(20Cr)
S= 10 ∑ (20Cr)
now a pretty common result is nc0² + nC1² + nC2² +.......+ nCn² = 2nCn (quite easy to prove, lemme know if you need help).
so, we have S= 10*(40C20)
KINDLY APPROVE :))
5 months ago
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