作业帮世上最有趣、牛的数学题
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世上最有趣、牛的数学题
世上最有趣、牛的数学题
世上最有趣、牛的数学题
假如
a=0.9999999999.
10a=9.99999999.
10a=9+0.99999999.
10a=9+a
9a=9
a=1
0.99999999.=1
sunny+day=Sunday
sinx/n
=six*n/n
=six
=6
令Ef[n] = f[n + 1], Δf[n] = f[n + 1] - f[n]
那么Δf[n] = Ef[n] - f[n]，Δf[n] = (E - 1)f[n]
即Δ = E - 1
故f[n] = E^nf[0] = (Δ + 1)^nf[0] = ΣC(n,k)Δ^kf[0]
比如f[n] = 1^2 + 2^2 + 3^2 + ... + n^2...
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令Ef[n] = f[n + 1], Δf[n] = f[n + 1] - f[n]
那么Δf[n] = Ef[n] - f[n]，Δf[n] = (E - 1)f[n]
即Δ = E - 1
故f[n] = E^nf[0] = (Δ + 1)^nf[0] = ΣC(n,k)Δ^kf[0]
比如f[n] = 1^2 + 2^2 + 3^2 + ... + n^2
Δ^0f[0] = 0
Δ^1f[0] = 1
Δ^2f[0] = 3
Δ^3f[0] = 2
Δ^kf[0] = 0, k > 3
所以f[n] = 1 ^ 2 + 2^2 + 3^2 + ... + n^2 = C(n, 1)*1+C(n, 2)*3+C(n, 3)*2 = n(n+1)(2n+1)/6
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