Find Sn for a series with tn equal to each value:
d) 2^(n+1)
Can somebody help me out :S
d) 2^(n+1)
Can somebody help me out :S
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t[1] + t[2] + t[3] + ... + t[x] =>
2^(1 + 1) + 2^(2 + 1) + 2^(3 + 1) + ... + 2^(x + 1)
2^2 + 2^3 + 2^4 + ... + 2^(x + 1) = S
Multiply everything by 2
2^3 + 2^4 + 2^5 + ... + 2^(x + 1) + 2^(x + 2) = 2S
2S - S = 2^(x + 2) - 2^2
S * (2 - 1) = 4 * 2^(x) - 4
S = 4 * (2^(x) - 1)
2^(1 + 1) + 2^(2 + 1) + 2^(3 + 1) + ... + 2^(x + 1)
2^2 + 2^3 + 2^4 + ... + 2^(x + 1) = S
Multiply everything by 2
2^3 + 2^4 + 2^5 + ... + 2^(x + 1) + 2^(x + 2) = 2S
2S - S = 2^(x + 2) - 2^2
S * (2 - 1) = 4 * 2^(x) - 4
S = 4 * (2^(x) - 1)
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t_n = 2^(n + 1)
S_n = 2^2 (1 - 2^(n + 2))/(1 - 2) = 4 (2^(n + 2) - 1)
S_n = 2^2 (1 - 2^(n + 2))/(1 - 2) = 4 (2^(n + 2) - 1)