The general term formula of the sequence {an} is an = 1 / √ n + √ n + 1. If the sum of the preceding terms is 10, then the number of terms n is Process

The general term formula of the sequence {an} is an = 1 / √ n + √ n + 1. If the sum of the preceding terms is 10, then the number of terms n is Process

First, the denominator is rationalized
an=1/[√n+√(n+1)]=√(n+1)-√n
Sn=a1+a2+...+an
=√2-√1+√3-√2+...+√n-√(n-1)+√(n+1)-√n
=√(n+1)-1
From the meaning of the title, we can get the conclusion
√(n+1)-1=10
√(n+1)=11
n+1=121
n=120

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

The sequence {an} satisfies A1 = a, an + 1 = can-c (n belongs to n *), a and C are real numbers, and C is not equal to 0. Find the general term formula of the sequence {an}

A (n + 1) = can-ca2 = ca1-c = AC can = Ca (n-1) - Ca (n + 1) - an = C [an-a (n-1)] let BN = a (n + 1) - an, B1 = a2-a1 = ac-c-abn = CB (n-1) BN = B1 * C ^ (n-1) = (ac-c-a) * C ^ (n-1) a (n + 1) - an = (ac-c-a) * C ^ (n-1) an-a (n-1) = (ac-c-a) * C ^ (n-2) a (n-1) - A (n-2) = (ac-c

How many centimeters is 43 inches, and what are the length and width?
How many centimeters is the 43 inch of the picture, and how much is the length and width?

43 inches is diagonal

There is a story book. Xiaohua read 5 / 16 of the whole book on the first day and 4 / 5 of the first day on the second day. He read 54 pages in two days. How many pages are left?

Suppose the whole book has x pages
5/16X+5/16X*4/5=54
X=96
Remaining: 96-54 = 42 (page)
A: there are 42 Pages in the book

If the polynomial (- A-1) x to the 5th power - 1 / 3 x to the B power + X-1 is a quartic trinomial of X, then the value of AB is
(- A-1) x ^ 5-3 / 1 x ^ B + X-1

On the quartic trinomial of X, the highest term can only be four times
The coefficient of the fifth term is 0: the fifth power of (- A-1) x, - A-1 = 0, - a = 1, a = - 1
And the remaining - 1 / 3 x to the power B + X-1
Only the B power of - 1 / 3 x can be a term of degree 4
be
b=4
ab=-4

The distance from a to B is 400 kilometers. A car starts from a and travels 225 kilometers in 3 hours. At this speed, can it reach B in 5 hours?

225÷3×5
=75×5
=375 km

How many points on the number axis that are less than 4 from the origin and represent integers? How many integers with absolute value not greater than 4? Are they?
How many points on the number axis are less than 4 from the origin and represent integers?
How many integers have absolute value less than 4? What are they?

There are 7 points on the number axis which are less than 4 from the origin and represent integers, - 3, - 2, - 1,0,1,2,3. There are 7 integers whose absolute value is not more than 4, which are also - 3, - 2, - 1,0,1,2,3. The absolute value is the distance between the point and the origin on the number axis

It takes 10 hours for a bus to go from city a to city B, and 8 hours for a truck to go from city a to city B. the two vehicles set out at the same time, facing each other and meeting each other in a few hours

1 / 10 + 1 / 8 = 1 / 9 / 40 = 40 / 9 hours

A is a rational number that is not 1. Let's subtract 1 / A from 1 to become the reciprocal of the difference of A
Definition: A is a rational number that is not 1. We call 1 / 1-A the inverse of A. for example, the inverse of 2 is 1 / 1-2 = - 1, the inverse of - 1 is 1 / 1 + 1 = 1 / 2. We know A1 = - 1 / 3, A2 is the inverse of A1, A3 is the inverse of A2, A4 is the inverse of A3,... And so on, what is A2010?

a1=-1/3
a2=1/4/3=3/4
a3=4
a4=-1/3
Is a sequence of three number cycles
2010=3*670
a2010=a3=4