Dear sir/madam,

Can you please explain to this question from AP

If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)

Open in App

Solution

let the common difference of this series is d & first term is a then

S_m = n = m/2 [ 2a + (m-1)d ]

2n/m = 2a + (m-1)d ......................1

S_n = m = n/2 [ 2a + (n-1)d ]

2m/n = 2a + (n-1)d ........................2

Subtracting both equations ,

2(n/m - m/n) = d(m-n)

d = -2[n+m/nm] ...................3

now , S_m+n = (m+n)/2 [ 2a + (m+n-1)d ]

S_m+n (2/m+n) = 2a + (m+n-1)d .......................4

eq 4 - eq 2

S_m+n (2/m+n) - 2m/n = d(m)

Putting value of d from eq 3 we get

S_m+n (2/m+n) = -2 or

S_m+n = -(m+n)

Suggest Corrections

Similar questions

Q. If

S_{n} = n^{2} p

and

S_{m} = m^{2} p

m \neq n

in an A.P., prove that

S_{n} = p^{3}

Q. If S_n = n² p and S_m = m² p, m ≠ n, in an A.P., prove that S_p = p³.

Q. If

S_{n} = n^{2} p

and

S_{m} = m^{2} p

m \neq n

, in A.P., then

S_{p}

is?

Dear Sir / Madam , Can you explain "diffusion" in very simple layman language .

Thanks & Regards

If $S_{n}$ denotes the sum of first n terms of an A.P. $< a_{n} >$ such that $\frac{S_{m}}{S_{n}} = \frac{m^{2}}{n^{2}}$ , then $\frac{a_{m}}{a_{n}} =$

Join BYJU'S Learning Program

Dear sir/madam, Can you please explain to this question from AP If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)

Dear sir/madam,

Can you please explain to this question from AP

If s(m)=n, s(n)=m prove that s(m+n)=-(m+n)