Question

Why is 1.1!+2.2!=5? But 1.1!+2.2!+3.3!=23? Explain in detail please

Answer 1

Answer:

Step-by-step explanation:

1!=1

2!=1*2=2

3!=1*2*3=6

Now

1.1!+2.2!=1*1+2*2=1+4=5

and 1.1!+2.2!+3.3!=1*1+2*2+3*6=1+4+18=23

Answer 2

Answer :-

Before coming to the Questions :-

♦ We should know about what is n! before start solving it .

» n! means n factorial

♦ Now what is factorial ?

» Factorial is nothing but successive multiplication of n natural numbers starting from 1 to n .

Factorials are represented by

$\lfloor n$

Or by n!

Now coming to the question :-

We have got to explain why

(i) 1 × 1! + 2 × 2! = 5

and

(ii) 1 × 1! + 2 × 2! + 3 × 3! = 23

Let us expand the first expression according to the factorial rules :-

→ (1 × 1) + (2 × 1 × 2) = 5

→ 1 + 4 = 5

→ 5 = 5

Now let us expand our second expression according to factorial rules :-

→ (1 × 1) + (2 × 1 × 2) + (3 × 1 × 2 × 3) = 23

→1 + 4 + 18 = 23

→ 23 = 23

So as we have got the same result , hence our explanation was right .