Arithmetic and Geometric Progressions

If the m^th term of a G.P. be n and the n^th be m, then that the (m+n)^th term is n^m/m-n/m^n/m-n.

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In a G.P. if the (p+q)^th term is m and the (p-q)^th term is n, prove that the p^th term is √mn

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Sum the following series: 1024 + 512 + 256 + ------------- to 15 terms.

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Sum the following series: 1 - 1/2 + 1/4 - 1/8 + ------------- to 12 terms.

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Sum the following series: 1 1/2 + 2 1/4 + 3 3/8 + ------------- to 8 terms.

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Sum the following series: √2 + √6 + √18 + ------------- to 10 terms.

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Sum the n terms series: 1/√3 + 1 + 3√3 + -----------.

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Sum the n terms series: 2 1/2 - 1 + 2/5 - -----------.

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Sum the n terms series: 0.3 + 0.03 + 0.003 + -----------.

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Sum the n terms series: (a + b) + (a² + 2b) + (a³ + 3b) + -----------.

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