Question

Sm=Sn(m≠n)show that (m+n)=0​

Answer 1

Step-by-step explanation:

Sm = Sn

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

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

m(2a + md -d) = n(2a + nd - d)

2am + m²d - md = 2an + n²d - nd

2a(m-n) + (m²-n²)d - md + nd = 0

2a(m-n) + (m²-n²)d - d(m - n) = 0

2a(m-n)+(m-n)(m+n)d - d(m-n) = 0

(m-n)(2a + (m+n)d - d) = 0

(m-n)(2a + md + nd - d) = 0

(m-n)( 2a + ((m+n) - 1)d) = 0