if in an AP the sum of first m terms is n and thr sum of its first n terms is m, then prove that the sum of its first (m+n) terms

2 thoughts on “if in an AP the sum of first m terms is n and thr sum of its first n terms is m, then prove that the sum of its first (m+n) terms”

1. Answer:

   [tex]S_m = n[/tex]

   [tex] \implies \: S_m = \frac{m}{2} (2a + (m – 1)d) = n \: – – – (i)[/tex]

   [tex]S_n = m[/tex]

   [tex] \implies \: S_n = \frac{n}{2} (2a + (n – 1)d) = m \: – – – – – (ii)[/tex]

   [tex]S_{(m + n)} = \frac{(m + n)}{2} (2a + (m + n – 1)d) \\ [/tex]

   [tex]eq \: (i) – eq(ii)[/tex]

   [tex]( \frac{m}{2} (2a + (m – 1)d) )- ( \frac{n}{2} (2a + (n – 1)d) = n – m\\ \\ [/tex]

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2. Answer:

   Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

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