All categories

2 years ago

1!+2(2!)+3(3!)+...+n(n!)=(n+1)!-1

Mathematics

1 answer:

anyanavicka [17]2 years ago

7 0

Step-by-step explanation:

OK, let's assume it this way:

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+...+(n+1)!-n!=(n+1)!-1!=(n+1)!-1

and boom problem solved

You might be interested in

For what value of a does 9 equal 1/27 a + 3

Yakvenalex [24]

Answer:

a = 162

Step-by-step explanation:

9 = 1/27 a +3

Subtract 3 from each side

9-3 = 1/27 a +3-3

6 = 1/27 a

Multiply each side by 27

6*27 = 1/27 a *27

162 = a

6 0

3 years ago

Read 2 more answers

What is the value of the expression x÷y when x = 30 and y = 18?

Eduardwww [97]

Answer:

5/3 or 1.66 or 1 2/3

Step-by-step explanation:

30/18 you can simply it to the factor of 6 or use a calc

5/3 if the person asks in fraction form and if they say that it can't be an improper fraction then it is 1 2/3 or get 1.6666 in calcutor

7 0

3 years ago

a high driver stands on a cliff 150 feet above sea level. he dives into the sea and goes 15 feet below the water. what is the di

natulia [17]

Start with the 150 and then add the 15, 165

3 0

3 years ago

Read 2 more answers

Please aswer this. Thank you!

mamaluj [8]

Answer:

4 pairs of sock and a little bit of left over change.

Step-by-step explanation:

24.95 + 5.95x = 50

-24.95 -24.95

5.95x=25.05

/5.95 /5.95

x = 4.21

We drop the 0.21 because you cant have 0.21 pairs of socks and we get:

x=4

6 0

2 years ago

Read 2 more answers

C. Line m is a perpendicular bisector. If EG=12 and FG=5, of then how long is:

strojnjashka [21]

Answer:

$EF = 13$

$GH = 5$

$EH = 13$

Step-by-step explanation:

Given

The attached figure

$EG = 12$

$FG = 5$

Solving (a): EF

Since m is a perpendicular bisector, then <EGF and <EGH are right-angled.

So, EF will be calculated using Pythagoras theorem which states:

$EF^2 = EG^2 + FG^2$

$EF^2 = 12^2 + 5^2$

$EF^2 = 144 + 25$

$EF^2 = 169$

Take the positive square roots of both sides

$EF = \sqrt{169$

$EF = 13$

Solving (b): GH

Since m is a perpendicular bisector, then GH = FG

$FG = 5$

$GH = FG$

$GH = 5$

Solving (c): EH

Since m is a perpendicular bisector, then EH = EF

$EF = 13$

$EH = EF$

$EH = 13$

4 0

3 years ago

1!+2(2!)+3(3!)+...+n(n!)=(n+1)!-1​

1!+2(2!)+3(3!)+...+n(n!)=(n+1)!-1