Question

Observe That
1/1.3 = 1/3
1/1.3 + 1/3.5 = 2/5
1/1.3 + 1/3.5 + 1/5.7 = 3/7
1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 = 4/9
Guess A General Formula And Prove It By Mathematical Induction.

Answer 1

Step-by-step explanation:

Let S=

1.3

1

+

3.5

1

+

5.7

1

++

(2n−1)(2n+1)

1

=

2

1

[

1.3

3−1

+

3.5

5−3

+

5.7

7−5

++

(2n−1)(2n+1)

2n+1−(2n−1)

]

=

2

1

[1−

3

1

+

3

1

−

5

1

+

5

1

−

7

1

+

7

1

−−

(2n−1)

1

+

(2n−1)

1

−

(2n+1)

1

]

=

2

1

(1−

2n+1

1

)=

2n+1

n