Can you tell me what log means?

Log is the abbreviation of log10, if it is mathematics

Log function related definitions common sense law operation law
RT
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A ^ (log (a) (b)) = b

Logarithmic identity, you want to, let log (a) (b) = x, the transformation is a ^ x = B, the original formula A ^ (log (a) (b)) = a ^ x = B

Log (a ^ b) = b * log a how is this derived?

The formula log a (MN) = log a (m) + log a (n) log (a ^ b) = log (AAA... AAA) has b, a = log a + log a + log a +... + log a has b = b * log a

The known sequence {an} satisfies A1 = 1, log (2) a_ {n+1}=log(2)a_ n+1 .
Under the condition (log (2) a_ {n+1}=log(2)a_ N + 1) is how to draw a conclusion_ {n+1}=2a_ N?

log2(a[n+1])=log2(an)+1=log2(an)+log2(2)=log2(2an)
So a [n + 1] = 2An
That is, the sequence {an} is an equal ratio sequence, that is, an = a1q ^ (n-1) = 1 * 2 ^ (n-1)

Given the first few terms of sequence an and Sn, and satisfying log with 2 as the base (1 + SN) = n + 1, find the general term formula of {an],

log2（1+Sn)=n+1
2^n+1=1+sn
sn=2^(n+1）-1
an=sn-sn-1=2^(n+1）-1-（2^n-1)=2^n-2

For the general term UN of a series, when n →∞, if UN → 0, what is the convergence and divergence of the series? On the contrary, if the series converges, does the general term UN tend to 0?

If UN → 0, the series converges;
On the contrary, no one stipulates that the limit of sequence must be 0
1,1+1/1,1+1/2,1+1/3…… Convergence to 1

Set 0
Analysis of finding B and D

B. For example, when n = 2K, u [n] = 1 / (2n), when n = 2k-1, u [n] = 0. So ∑ {1 ≤ n} (- 1) ^ n · u [n] = ∑ {1 ≤ K} u [2K] = ∑ {1 ≤ K} 1 / (4K), divergent. D. correct, from 0 ≤ u [n] < 1 / N, there are 0 ≤ u [n] & # 178; < 1 / N & # 178;. According to the comparative discriminant method

Does the series with the general term UN = one nth converge?

It is proved that if the series ∑ UN ^ 2 and ∑ VN ^ 2 converge, then ∑ (UN / N) converges

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Can you tell me what log means?