Question

How many terms of the series 1 + 2 + 4 +….. sum to 2047

Answer 1

Let, n consecutive terms are needed to yield the sum of 1022.

Then, we have,

2+4+8+….upto n terms=1022

⟹2⋅(2n−1)2–1=1022

[As, the first term and common ratio of the GP are 2 and 2 respectively.]

⟹2n−1=511

⟹2n=512=29

∴n=9.†

Hence, 9 consecutive terms are needed to yield the sum of 1022.

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