Given a simple proof that ∑k=0n3ak=3∑k=0nak

We have proved ∑k=0n3ak=3∑k=0nak

Q. 59 - Calculus | StudyQuestionHub

Given a simple proof that $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$

Verified

Answer

We have proved $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$

1Step 1: Given information

We are given a relation $\sum_{k = 0}^{n} 3 a_{k} = 3 \sum_{k = 0}^{n} a_{k}$ . We have to prove it

2Step 2: Proof

We have,

$\sum_{k = 0}^{n} 3 a_{k} = 3 a_{1} + 3 a_{2} + . . . . + 3 a_{n} = 3 (a_{1} + a_{2} + . . . . + a_{n}) = 3 \sum_{k = 0}^{n} a_{k} = R H S$

Hence proved