2^(n) lt n! ಗಾಗಿ ನಿಜವಾಗಿದೆ | ತರಗತಿ 12 | ಗಣಿತದ ತತ್ವ | ಗಣಿತ | ಡೌಟ್ನಟ್

2^(n) lt n! holds for

2 <= (1+ (1) / (n)) ^ (n) <3, n> = 1, n in N

nCr + 2.nC (r-1) + nC (r-2) = (n + 2) Cr (2 <= r <= n)

If P(x) = a _0 + a _1 x ^(2) + a _2 x^(4) + … + a _n x ^(2n) is a polynomial in a real variable x with 0 lt a _0 lt a _1 lt a _2 lt … lt a_n . Then, the function P (x) has

If 0 lt x lt pi/2 and sin^(n) x + cos^(n) x ge 1 , then