Math, asked by mrhacker56, 11 months ago

If the m term of an ap is 1/n and the n term is 1/m show that the sum of m and n term is 1/2 ( mn + 1)

Answers

Answered by Anonymous
5

Answer:

Refer to Attachment for Answer .

Solved by KarnShubham ❤️

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Answered by hotUsername
5

Answer:

→ aₘ = a + (m - 1)d = 1/n ___(1)

→ aₙ = a + (n - 1)d = 1/m ___(2)

Sₘₙ = (mn)/2 × [2a+(mn-1)d]

Substraction of (2) and (1),

→ nd - md = 1/m - 1/n

→ (n - m)d = (n - m)/mn

→d = 1/mn

→ a + (m - 1)d = 1/n

→ a + (m - 1)1/mn = 1/n

→ a + 1/n - 1/mn = 1/n

→ a = 1/mn = d

→ L.H.S ↓

→ Sₘₙ = (mn)/2 × [2a+(mn-1)d]

→ (mn)/2 × [2/mn+(mn-1)1/mn]

→ (mn)/2 × [2/mn + (mn)/mn - 1/mn]

→ mn/2 × [1/mn + 1]

→ 1/2 + mn/2

→ ½(mn + 1) =R.H.S

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