please kk dijawab beserta caranya

jawab
induksi matematis

a)
2 + 4 + 6 + 8 + ... + 2n = n(n + 1)
n = 1
=> 2n = n(n + 1)
=> 2(1) = 1(1 + 1)
=> 2 = 1(2)
=> 2 = 2 ......(terbukti)
n = k
2 + 4 + 6 + 8 + ... + 2k = k(k+ 1)
n = k + 1
2 + 4 + 6 + 8 + ... + 2k + 2(k + 1) = (k + 1)(k + 1 + 1)
=> 2k + 2(k + 1) = (k + 1)(k + 2)
=> k(k + 1) + 2(k + 1) = (k + 1)(k + 2)
=> (k + 1)(k + 2) = (k + 1)(k + 2)....(terbukti)

b)
1 + 2 + 4 + 8 + ... + 2^(n-1) = 2^(n) - 1
n = 1
=> 2^(n-1) = 2^(n) - 1
=> 2^(1-1) = 2^(1) - 1
=> 2^(0) = 2 - 1
=> 1 = 1 .....(terbukti)
n = k
1 + 2 + 4 + 8 + ... + 2^(k-1) = 2^(k) - 1
n = k + 1
1 + 2 + 4 + 8 + ... + 2^(k-1) + 2^(k+1-1) = 2^(k+1) - 1
=> 2^(k-1) + 2^(k) = 2^(k+1) - 1
=> 2^(k) - 1 + 2^(k) = 2^(k+1) - 1
=> 2^(k+1) - 1 = 2^(k+1) - 1 .....(terbukti)