The sum to n-1 terms of the series c0-2-c1-3-c2-4-c3-5- - isA- 1-n-2B- 1 -n-1n-2C- 1-nn-1D- 1-n-1

The correct option is B (1 x)^n = c_0 c_1 x + c_2 x^2 c_3 x^3 + ......n terms x(1 x)^n = c_0 x c_1 x^2 + c_2 x^3 c_3 x^4...... ∫_0^1 x (1 x)^n = ∫ (c_ ...

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Byju's Answer

Standard XII

Mathematics

A.G.P

The sum to n+...

Question

The sum to (n + 1) terms of the series $\frac{c_{0}}{2} - \frac{c_{1}}{3} + \frac{c_{2}}{4} - \frac{c_{3}}{5} + . . . . i s$

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Solution

The correct option is D
$(1 - x)^{n} = c_{0} - c_{1} x + c_{2} x^{2} - c_{3} x^{3} + . . . . . . n t e r m s x (1 - x)^{n} = c_{0} x - c_{1} x^{2} + c_{2} x^{3} - c_{3} x^{4} . . . . . . \int_{0}^{1} x (1 - x)^{n} = \int (c_{0} x - c_{1} x^{2} + c_{2} x^{3} - c_{3} x^{4} + . . . .) d x ∴ \frac{c_{0}}{2} - \frac{c_{1}}{3} + \frac{c_{2}}{4} - \frac{c_{3}}{5} + . . . . . . = \frac{1}{(n + 1) (n + 2)}$

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