The distributive law from algebra states that for all real numbers c,a1 and a2,we have `c(a_1+a_2)=c a_1+c a_2` Use this law and mathematical induction to prove that,for all natural numbers,`ngeq2`,if `c,a_1,a_2,....,`an are any real numbers,then `c(a_1+a_2+.....+a_n)=c a_1+c a_2+....+c a_n`

Explanation

Let P(n):`c(a_1+a_2+…+an)` = `ca_1+ca_2+…`+can ,for all natural numbers, `n >= 2`.
Step1: For n=2,

P(2)

LHS= `c(a_1 + a_2)`

RHS= `c a_1 + ca_2`

As, it is given that` c(a_1 + a_2)` = `c a_1 + ca_2`

Thus, P(2) is true.
Step2: For n=k,

Let P(k) be true

So, `c(a_1+a_2+…+a_k ) `= `ca_1+ca_2+…+ca_k `
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