Find the sum of the GP $(1 + x)^{21} + (1 + x)^{22} + . . . . . . (1 + x)^{30}$

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Solution

The correct option is A

The given sequence is geometrical progression with common ratio (1+x)
$(1 + x)^{21} + (1 + x)^{22} + . . . . . . (1 + x)^{30} = (1 + x)^{21} (1 + (1 + x)) + . . . . . (1 + x)^{9})$
= $(1 + x)^{21} (\frac{(1 + x)^{10} - 1}{(1 - x) - 1})$
= $(1 + x)^{21} (\frac{(1 + x)^{10} - 1}{x})$
= $(\frac{(1 + x)^{31} - (1 + x)^{21}}{x})$

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