Math, asked by sahoom73, 7 months ago

+D) (27)
11.13 +24+3.5+
+(2) solve by induction

Answers

Answered by Mystreymanish
0

Answer:

mark me as brainliest

Step-by-step explanation:

Answered by trilakshitha
0

Answer:

Let

P(n):

2.7

n

+

3.5

n

5

is divisible by 24

We note thatP(n)is true when

n=

1

, since

2.7+

3.5−

5=

24

. which is divisible by

24.

Assume that P(k) is true.

i.e.

2.7

k

+

3.5

k

5=

24q

when

q∈

N

-------------- ( 1 )

Now, we have to prove that

P(k+

1)

is true whenever

P(k) is true.

We have

2.7

k+1

+ 3.5

k+1

− 5

2.7

k

.7

1

+

3.5

k

.5

1

5

7[2.7

k

+

3.5

k

5−

3.5

k

+

5]+

3.5

k

.5−

5

7[24q−

3.5

k

+

5]+

15.5

k

5

24q−

21.5

k

+

35+

15.5

k

5

24q−

6.5

k

+

30

24q−

6(5

k

5)

24q−

6(4p)

[

(5

k

5)

is multiple of

4

]

24q−

24p

24(7p−

q)

24×

r;r=

7p−

q.

is some natural number ---------- ( 2 )

The expression on the R.H.S oof ( 1 ) is divisible by 24 . Thus

P(k+

1)

is true whenever P(k) is true.

Hence, by principle of mathematical induction , P(n)is true for all

n∈

N.

Step-by-step explanation:

Hi..

Hope it helps you...

Similar questions