The formula for the direction of the increasing series and the sum of the first n terms???

Solution: Observation.

respectively. 2,4,8,16,32，……Subtract 1 to get it.

So. an=2^n-1

So. The first n terms and sn=(2-1)+(4-1))+8-1))+16-1)......2^n-1)

2+4+8+……2^n）-n

2^（n+1）-n-2

Solution: It can be known from the meaning of the title.

a(n)-a(n-1)) (a(n-1)-a(n-2))=2 i.e. A number column is a proportional series.

And the first term is a2-a1=2

Old. a（n）-a（n-1）=2^（n-1）a（n-1）-a（n-2）=2^（n-2）a（2）-a(1)=2

The above equation can be obtained by adding the left and right respectively.

an=2^n-1

So. sn=2+4+..2^n-n=2^（n+1）-2-n

General Formula 2 to the nth power 1

The first n items and. 2 times n times - 1-n

Incrementing sequencesGeneral term formulasis an=a1+d, where d>0, for a series, if the value of each term from the second term of the series is not less than the value of the first term before it, then such a series is said to be an increasing volcanic sequence.

The formula for increasing the number series is calculatedThe formula for summing the increasing series is (first term + last term) * number of terms 2. Sequence summation sums numbers arranged according to a certain law. Finding the SN is essentially the formula for finding the pin-and-reserve general term, and attention should be paid to the understanding of its meaning.

The elements in a set are unordered, while the items in a sequence must be arranged in a certain order, i.e., they must be ordered.

A common method is the formula method.

Dislocation subtraction, reverse order addition, grouping, splitting, mathematical induction.

Summing of general terms and mergers. Number series is an important part of high school algebra and advanced mathematics.

The foundation. There is a fundamental difference between them: the elements in a set are different from each other, while the terms in a sequence can be the same.

Equations for the difference series.

Equations for the difference series.

The formula for the difference series is an=a1+(n-1)d

The sum of the first n terms is: sn=na1+n(n-1)d 2 if the tolerance d=1: sn=(a1+an)n 2 if m+n=p+q: am+an=ap+aq, if m+n=2p, then: am+an=2ap

The above n are positive integers.

Text translation. The value of the nth term an = first term + (number of terms - 1) tolerance.

The sum of the first n terms sn=first term + last term Number of terms (number of terms-1) tolerance 2 tolerance d=(an-a1) (n-1).

Number of Items = (Last Item - First Term) Tolerance + 1

When the number column is an odd number, the sum of the first n terms = the number of intermediate terms.

The number column is an even number of terms, find the first and last terms, add the first and last terms, divide it by the sum of 2 equal differences, and the formula for the middle term is 2an+1=an+an+2, where is the equal difference series.

Summary. Hello, it is a pleasure to answer for you - - the general term formula of the equal difference series.

an=a1＋(n－1)d

Promotional. an=am+(n－m)d

The first n terms of the equal difference series and the formula.

sn＝（a1+an）*n/2

sn=na1+n(n-1)d/2

Proportional sequence of general term formulas.

General formula: an=a1*q (n 1);

Promotional: an=am·q (n m);

Summation formula: sn=na1(q=1).

sn=[a1(1-q)^n]/(1-q)

Hope mine can help you, hope].

Know how to find the sum of the first n terms in the general term formula of a series.

Hello, it is a pleasure to answer for you - - the general term formula of the equal difference series.

an=a1＋(n－1)d

Promotional. an=am+(n－m)d

The first n terms of the equal difference series and the formula.

sn＝（a1+an）*n/2

sn=na1+n(n-1)d/2

Proportional sequence of general term formulas.

General formula: an=a1*q (n 1);

Promotional: an=am·q (n m);

Summation formula: sn=na1(q=1).

sn=[a1(1-q)^n]/(1-q)

Hope mine can help you, hope].

I won't use it. Wait a minute.

Classmate's formula tells you that you can't yet.

I don't know how to apply it to the problem, the formula has basically been memorized, I just don't know how to expand, should I write out the first n terms and each of the terms, or should I use another method?

Write out the first n items and write.

A general formula for a series of equal differences.

an=a1＋(n－1)d

Promotional. an=am+(n－m)d

The first n terms of the equal difference series and the formula.

sn＝（a1+an）*n/2

sn=na1+n(n-1)d/2

Proportional sequence of general term formulas.

General formula: an=a1*q (n 1);

Promotional: an=am·q (n m);

Summation formula: sn=na1(q=1).

sn=[a1(1-q)^n]/(1-q)

The iterative method, also known as the tossing method, is a process of continuously using the old value of a variable to recursively extrapolate the new value, and the iterative method corresponds to the direct method (or the one-time solution method), that is, to solve the problem at one time.

For example, in a series of equal differences, an+1=an+d:

an=an-1+d=（an-2+d）+d=（an-3+d）+d+d……

a1+（n-1）d

This is the iterative approach, and here is the simplest example.

The meaning of the iterative method is that the latter term is derived from the previous term, similar to the form of a(n+1)=f(an), generally the general term formula of this form will give an initial value, and then the subsequent terms can be found in turn, but it is usually necessary to turn it into the general general term form of an=f(n) in order to facilitate the calculation of terms and sn, etc., please refer to this document for details.

For example, in a series of equal differences, an+1=an+d

What does iteration mean?

an=an-1+d=（an-2+d）+d=（an-3+d）+d+d……

a1+（n-1）d

This is the iterative approach, and here is the simplest example.

When many complex sequences are not as easy to find as a series of equal differences, the formula for finding the general term often uses the iterative method.