The sum of values of r for which 18 Cr-2+2 ⋅ 18 Cr-1+ 18 Cr ≥ 20 C13

Question

The sum of values of r for which 18 Cr-2+2 ⋅ 18 Cr-1+ 18 Cr ≥ 20 C13 (A) 40 (B) 50 (C) 60 (D) 70

Tardigrade Admin · Accepted Answer

Using formula n Cr+ n Cr-1= n+1 Cr 18 Cr-2+ 18 Cr-1+ 18 Cr-1+ 18 Cr ≥ 20 C13 19 Cr-1+ 19 Cr ≥ 20 C13 20 Cr ≥ 20 C13 text or 20 C20-r ≥ 20 C13 r=7,8,9,10,11,12,13 Sum of all values of r=70.

Q. The sum of values of $r$ for which $^{18} C_{r - 2} + 2 \cdot^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}$

$40$

$50$

$60$

$70$

Q. The sum of values of r for which 18Cr−2​+2⋅18Cr−1​+18Cr​≥20C13​

40

50

60

70

Using formula nCr​+nCr−1​=n+1Cr​ 18Cr−2​+18Cr−1​+18Cr−1​+18Cr​≥20C13​ 19Cr−1​+19Cr​≥20C13​ 20Cr​≥20C13​ or 20C20−r​≥20C13​ r=7,8,9,10,11,12,13 Sum of all values of r=70.

Q. The sum of values of $r$ for which $^{18} C_{r - 2} + 2 \cdot^{18} C_{r - 1} +^{18} C_{r} \geq^{20} C_{13}$

$40$

$50$

$60$

$70$