Question

[Arithmetic Progression, Class 10]
Q. If mth term of an AP is 1/n and the nth term is 1/m then find the sum of its first mn terms.

Best Explanation will get Brainliest.

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Answer 1

☺️$\large\bf\underline\orange{\:Toh\:Kaise\:Hai\:Aap\:Log\:}$✌️

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$\huge\bf\red{Question\::-}$

If mth term of an AP is 1/n and the nth term is 1/m then find the sum of its first mn terms.

$\huge\bf\purple{Given\::-}$

• mth term of an ap is 1/n and nth term is 1/m.

$\huge\bf\blue{To\:Find\::-}$

• The sum of first mn terms.

$\huge\bf\pink{Solution\::-}$

Let the 1st term is a and common difference is d of the given A.P.

ATQ

➳ a(m) = a + (m - 1)d = 1/n ______①

➳ a(n) = a + (n - 1)d = 1/m ______②

On Subtracting Eq (ii) from (i), we get

➳ (m - 1)d = 1/n - 1/m = m - n/mn

➳ d = 1/mn

➳ a = 1/mn

Now, S(mn) = mn/2[2 × 1/mn + (mn - 1)1/mn]

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

S(mn) = mn/2[1/mn + 1]

= 1/2[mn + 1]

$\small\bold{The \:sum\: of\: first\: mn \:terms\: is\: \frac{1}{2[mn + 1]} }$

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Answer 2

Answer:

$ur \: answer \: was \: given \: by \: my \: brother \: above$