数列{an}满足an+1+（-1）nan=2n-1，则{an}的前60项和为 ___ ．_数学解答

数列{a_n}满足a_n+1+（-1）ⁿa_n=2n-1，则{a_n}的前60项和为 ___ ．

人气：231 ℃　时间：2020-10-01 19:18:52

解答

∵an+1+(-1)nan=2n-1，∴an+1=2n-1-(-1)nan令bn+1=a4n+1+a4n+2+a4n+3+a4n+4，a4n+1+a4n+3=（a4n+3+a4n+2）-（a4n+2-a4n+1）=2，a4n+2+a4n+4=（a4n+4-a4n+3）+（a4n+3+a4n+2）=16n+8，则bn+1=a4n+1+a4n+2+a4n+3+a4n+4...