7、证明题(本题满分8分)设数列{an},{b}满足0<an,bn< (n=1,2,…),且 cos an-an= cos bn,由∑=1bn收敛,证明 (1)an→0(n→∞),(2)∑1a收敛 第7页(共7页)7!y²K£K˜©8©§ Í{an}, {bn}˜v0 < an, bn < π 2 (n = 1, 2, . . .)ßÖcos an − an = cos bnßd P∞ n=1 bn¬Òßy² (1) an → 0 (n → ∞), (2) P∞ n=1 an bn¬Ò" 17ê (
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