2+2²+2³+2⁴+2n give the general formula
Answers
Answered by
3
Assume, for n = k
2 + 2^2 + 2^3 + 2^4 + ... + 2^k
Let n = k + 1.
2 + 2^2 + 2^3 + 2^4 + ... + 2^k + 2^{k+1 }
= [2 + 2^2 + 2^3 + 2^4 + ... + 2^k] + 2^{k+1 }
= [2^{k+1} – 2] + 2^{k+1 }
= 2×2{k+1} – 2
= 2^1×2^{k+1} – 2
= 2^{k+1}+1 – 2
= 2^(k+1)+1 – 2
so n=k+1
=2^n+1 - 2
2 + 2^2 + 2^3 + 2^4 + ... + 2^k
Let n = k + 1.
2 + 2^2 + 2^3 + 2^4 + ... + 2^k + 2^{k+1 }
= [2 + 2^2 + 2^3 + 2^4 + ... + 2^k] + 2^{k+1 }
= [2^{k+1} – 2] + 2^{k+1 }
= 2×2{k+1} – 2
= 2^1×2^{k+1} – 2
= 2^{k+1}+1 – 2
= 2^(k+1)+1 – 2
so n=k+1
=2^n+1 - 2
brainly38:
but only u answered the question
no one else did
??
oh okok
hmm
if the answer is correct mark it as brainliest
ok
whats the answer
i dont know
okok
Similar questions