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G.P 1+2+4+8+16+....+n

How does the sum of the above GP come down to 2n - 1?
Please explain.

The geometric series is 1+2+4+8+....+2^k
Let’s assume that 2^k = n
`2^0+2^1+2^2…+2^k = 2^(k+1)-1

= 2^k * 2^1-1

Substituting n for 2^k we get,
= 2n-1

Anum Hassan|Developer Advocate
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