`A=[[1 ,1], [1, 1]]` then prove that `A^(100)=2^(99)A`

If f(x) = (x ^(100))/( 100) +( x^(99))/( 99) +( x^(98))/( 98) +---+ (x^(2))/( 2) + x+1 then prove that f^(1) =100 f^(1) (0 )

If A=det[[1,11,1]] and A^(100)=lambda^(99)A, then the value of lambda is

If f(x)=(x^(100))/(100)+(x^(99))/(99)+(x^(98))/(98) +------+ x^(2)/2+x+1 then prove that f^(1) (1)=100. f^(1)(0)

Using the sum of G.P., prove that a^(n)+b^(n)(a,binN) is divisble by a+b for odd natural numbers n. Hence prove that 1^(99)+2^(99)+….100^(99) is divisble by 10100

Using the sum of G.P., prove that a^(n)+b^(n)(a,binN) is divisble by a+b for odd natural numbers n. Hence prove that 1^(99)+2^(99)+….100^(99) is divisble by 10100

Using the sum of G.P., prove that a^(n)+b^(n)(a,binN) is divisble by a+b for odd natural numbers n. Hence prove that 1^(99)+2^(99)+….100^(99) is divisble by 10100

Let A = [[1, (-1-isqrt(3))/(2)],[(-1+isqrt(3))/(2),1]] . Then , A^(100) is equal to a) 2^(100)A b) 2^(99)A c) 2^(98)A d)A

Consider the real valued function h:{0, 1, 2 …..100} to R such that h(0)=5, h(100)=20 and satisfying h(p)=(1)/(2) {h(p+1)+h(p-1)} for every p=1,2 …. 99. Then he value of h(1) +h(99) is

For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+ .......+(x^(2))/2)+x+1 . prove that f(1)=100f(0).

For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+...+(x^2)/2+x+1 . Prove that f^(prime)(1)=100f^(prime)(0) .