Sum of the series 3+5+9+17+33+......to n terms is
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Answered by
8
Sn = (2+1) + (4+1) + (8+1) + (16+1) +……+ upto n terms
Sn = (1 + 1 + 1 + 1 + …unto n terms) + (2 + 4 + 8 + 16 + …upto nth power of 2)
In above formula,
2 + 4 + 8 + 16…. is a G.P.
It’s sum of first n terms is given by 2*(2^n-1)/(2-1) = 2^(n+1) – 2 (using G.P. formula)
Sn = n + 2*(2^n – 1)
Sn = 2^(n+1) + n -2
I hope it help you
Sn = (1 + 1 + 1 + 1 + …unto n terms) + (2 + 4 + 8 + 16 + …upto nth power of 2)
In above formula,
2 + 4 + 8 + 16…. is a G.P.
It’s sum of first n terms is given by 2*(2^n-1)/(2-1) = 2^(n+1) – 2 (using G.P. formula)
Sn = n + 2*(2^n – 1)
Sn = 2^(n+1) + n -2
I hope it help you
Answered by
2
Answer:
S=2n+1−2+n .
The sequence can be defined as: ak=2k+1,k∈I,k≥1.
Now we want the sum.
S=∑k=1n(2k+1)=∑k=1n2k+∑k=1n1=∑k=1n2k+n
Let:Then:And:T2TT===2+22+23+⋯+2n−1+2n22+23+24+⋯+2n+2n+12T−T=2n+1−2
So: S=∑k=1n2k+n=T+n=2n+1−2+n
Step-by-step explanation:
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