Question

from sum of AP CHAPTER​

Answer 1

Step-by-step explanation:

= m/2×[a(1)+a(m)]

= m/2 [2a(1)+(m−a)d] (1)

Sum of next n terms

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

= n/2[2a(1)+(2m+n−1)d] (2)

Sum of next p terms

= p/2[a(m+n+1)+a(m+n+p)]

= p/2[2a(1)+(2m+2n+p−1)d] (3)

S( 2/n - 2/m )=(m+n)d (4)

S( 2/p - 2/m )=(m+p)d (5)

On dividing, we get

m+p/m+n = (1/n - 1/m) / (1/p - 1/m)

m+p/m+n = (1/m - 1/n) - (1/m - 1/p)

(m+n) (1/m - 1/p) - (m+p) (1/m - 1/n) = 0

Hope it helps

Thankyou ✌