Question

If the mth term of an A P is 1/n and the nth term is 1/m, show the sum of its first(mn) terms is1/2(mn + 1).

Answer 1

Answer:

Step-by-step explanation:

Sol.

Let a be the first term and d be the common difference. then,

tm= 1/n

a+(m-1)d=1/n -eqn(i)

tn= 1/m

a+(n-1)d=1/m-eqn-(ii)

Subtracting (ii) from (i), we get

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

[a+(m-1)d-a-(n-1)d= m-n/mn

[d(m-1-n+1)]= m-n/mn

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

d=1/mn.

Putting d=1/mn in eqn (i), we get

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

a+(m-1)×1/mn=1/n

a+(m-1)/mn=1/n

amn+m-1/mn=1/n

amn+m-1/1=mn/n

amn+m-1=m

amn-1=m-m

amn-1=0

amn=1

a=1/mn.

Therefore,

Smn= mn/2[2a+(mn-1)d]

mn/2[2×1/mn+(mn-1)×1/mn

mn/2[2/mn+mn-1/mn]

mn/2[2+mn-1/mn]

mn/2[mn+1/mn]

mn/2×mn+1/mn

mn+1/2 ans.

Answer 2

Answer:

Step-by-step explanation: