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Find the sum to $n$ terms of each of the series in Exercises.$$1 \times 2+2 \times 3+3 \times 4+4 \times 5+\ldots$$

Precalculus

Chapter 9

Sequences and Series

Section 4

Arithmetic Progression (A.P.)

Introduction to Sequences and Series

Johns Hopkins University

Campbell University

Piedmont College

Harvey Mudd College

Lectures

02:18

A sequence is a collection…

01:42

06:22

Find the sum of each serie…

06:09

12:28

06:46

01:29

Find the sum of the first …

04:05

01:31

Find the sum of each arith…

04:26

01:13

01:43

02:14

00:31

05:39

For each sum, find the num…

01:39

03:51

01:14

02:42

04:24

01:06

Use a formula for $S_{n}$ …

02:22

we have lowered the number one. What we need to fine. But there are some to in terms of the threes given as one into two plus two and 23 players. Three into four plus four into five and so on. Okay. Okay. So first of all this the in term of the city's Bill Burton is this is N. And plus one and in two and plus one. Quite simple. So a zen will be equal to submission of the N. We're an equal to one to win. So submission and equal to one to end and in two and plus one submission of an equal to one to end and square blessing. Okay so this is submission of and equal to one to N N. Square plus the mission of an equal to one to end. And this is they squared. So we have the formula for this and into and plus one into 21 plus one by six plus an into and plus one by two. So N into unpleasant but you will be taken as common. So this will be 20 plus one by three plus one. This means and into and plus one by two. And this will be 20 plus four two. N plus four by three and in two and plus one into two. So this will be and plus two by three. So two and here it was too it gave cancel out. So finally as N will be equal to and in two and plus one in two and plus two by three. They should be the answer. Thank you so much. Have a nice day.

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