Question

in ap Sm/Sn=m4/n4 then prove that Tm+1/Tn+1=(2m+1)^3/(2n+1)3​

Answer 1

Answer:

Given relation implied that

2

n

[2a+(n−1)d]

2

m

[2a+(m−1)d]

=

n

4

m

4

or

a+

2

n−1

d

a+

2

m−1

d

=

n

3

m

3

(1)

Now

T

N+1

T

M+1

=

a+Nd

a+Md

where

M=

2

m−1

;N=

2

n−1

or m=2M+1,n=2N+1

∴

T

N+1

T

M+1

=

(2N+1)

3

(2M+1)

3

or

T

n+1

T

m+1

=

(2n+1)

3

(2m+1)

3

.