How to solve this by mathematical induction? can someone help me ^^​

Below.

Step-by-step explanation:

First check if its true for n = 1:-

∑1(1!) = 1*1 = 1

(n + 1)! - 1 = 2! - 1 = 2 - 1

= 1.

So its true for n = 1.

Suppose it's true for a specific value n = k, then we have

∑k(k!) = (k + 1)! - 1

The (k + 1)th term is (k + 1)(k + 1)!

So ∑k+1(k+1!) =  (k + 1)! - 1 +  (k + 1)(k + 1)!

= (k + 1)(k + 1)!- 1.

- this result is the same as the result  for ∑k(k!)  except that the k is replaced by k+1. So if its true for n = k then its also true for n = k+1.

We have shown that the formula is true for n = 1 so therefore it is true for 1, 2, 3, 4... (all whole numbers).

This concludes the proof.

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