Five marks exercise problems II — task. Mathematics State Board, Class 10.

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1. If the first term of an infinite G.P. is \(8\) and its sum to infinity is \(\frac{32}{3}\) then find the common ratio.

Answer:

The common ratio \(=\)

\frac{i}{i}

2. Find the sum in \(n\) terms of the series.

(i) \(0.4 + 0.44 + 0.444 + … \) to \(n\) terms

The sum of the series \(=\)

\frac{i}{i} i - \frac{i}{i} (i - {(\frac{i}{i})}^{i})

[Note: Enter coefficients and variables in separate boxes.]

(ii) \(3 + 33 + 333 + … \) to \(n\) terms

The sum of the series \(=\)

\frac{i (i^{i} - 1)}{i} - \frac{i}{i}

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6. Five marks exercise problems II