Grade 11Algebra
The value of 30 C 0 - 30 C 1 + 30 C 2 - 30 C 3 +...+30 C 10 is
The value of 30 C 0 - 30 C 1 + 30 C 2 - 30 C 3 +...+30 C 10 is
2 Answers
Aditya Gupta
Note that coeff of x^10 in Y= (30C0.x^0 – 30C1.x^1 + …. + 30C30.x^30)*(1+x+x^2+.......) will be the reqd sum.
Y= (1 – x)^30.(1/(1 – x)) (using BT and infinite GP sum)
or Y= (1 – x)^29
so, coeff of x^10 is 29C10.
Thus, sum= 29C10.
KINDLY APPROVE :))
Ram Kushwah
We know that
(1+x)n = ⁿC₀x⁰ + ⁿC1x+ ⁿC2x2+ ⁿC3x3+.....................................+ ⁿCnxn
Putting x = -1 we get
(1-1)n = ⁿC₀(-1)⁰ + ⁿC1(-1)+ ⁿC2(-1)2+ⁿC3(-1)3+.........................+ ⁿCn(-1)n
(1-1)n = ⁿC₀ - ⁿC1+ ⁿC2 - ⁿC3+.....................................+(-1)n ⁿCn
Further on plugging n=30 we get
30C₀ - 30C1+ 30C2 - 30C3+..................+(-1)30 x 30C30 =030
OR 30C₀ - 30C1 + 30C2 - 30C3+..................+ 30C30 = 0
Thus answer = 0
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago