The general term formula of sequence {an} is an = 1n (n + 1) (n ∈ n *). If the sum of the first n terms is 1011, then the number of terms is______ ．

The general term formula of sequence {an} is an = 1n (n + 1) (n ∈ n *). If the sum of the first n terms is 1011, then the number of terms is______ ．

∵an＝1n(n+1)＝1n−1n+1∴Sn=a1+a2+… +an=1−12+12−13+… +1n − 1n + 1 = 1 − 1n + 1 = NN + 1 ｛ NN + 1 = 1011 ｛ n = 10, so the answer is: 10

Given the sequence {an}, an is not equal to 0, A1 = 3, (1 / an + 1) = 2 + (1 / an), n is a natural number, find the formula of an
Given the sequence {an}, an is not equal to 0, A1 = 3, (1 / an + 1) = 2 + (1 / an), n is a natural number, and the formula [n + 1] is the subscript

Let 1 / an = BN
Then (1 / an + 1) = 2 + (1 / an)
It can be rewritten as
bn+1=2+bn
a1=3
b1=1/3
So BN = (6n-5) / 3
So an = 3 / (6n-5)

In the sequence {an}, A1 = 1 / 2, a (n + 1) = C * an + 1-C, n belongs to natural number, where C is a real number, and C is not equal to 0 (1)
(2) let C = 1 / 2, BNN (1-an), n belong to natural number, and find the sum SN of the first n terms of sequence {BN}

Because a (n + 1) - 1 = C * an + 1-c-1 = C * (an-1), when n > 2, the ratio of each term to the previous term is constant, so {an-1} is an equal ratio sequence. An = (- 0.5) C ^ (n-1) + 1
There seems to be a problem in question 2, indicating that the white dot C = 1 / 2, BNN (1-an),