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判定级数收敛性∑(㏑^n2/2^n 1/3^n)

收敛. ∑2^n/3^n是公比为2/3的等比级数,收敛. ∑1/3^n是公比为1/3的等比级数,收敛. 所以,原级数收敛.

以上,请采纳。

(0,π/2)∫dθ/(sinθ+cosθ) =(0,π/2)∫dθ/[√2sin(θ+π/4)] =(0,π/2)∫√2/2*csc(θ+π/4)dθ 换元θ+π/4=x =√2/2*(π/4,3π/4)∫cscxdx 又cscx在(π/4,3π/4)上连续 =√2/2*(π/4,3π/4)ln|cscx-cotx| =√2/2*ln|(√2+1)/(√2-1)| =√2/2*ln(√2+1)^2=√2ln(√2+1) 1。lim(...

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