Discussion

Explanation:

Given, f(x + y) = f(x) + f(y)

Substitute y = 0

⇒ f(x + 0) = f(x) + f(0)

⇒ f(0) = 0

Now, substitute x = y = 1, we get

f(1 + 1) = f(1) + f(1)

⇒ f(2) = 2f(1)

Now, substitute x = 2 and y = 1, we get

f(2 + 1) = f(2) + f(1) = 2f(1) + f(1) = 3f(1)

∴ f(3) = 3f(1)

Now, substitute x = 3 and y = 1, we get

f(3 + 1) = f(3) + f(1) = 3f(1) + f(1) = 4f(1)

∴ f(4) = 4f(1)

By observing the pattern, we can say that

f(x) = x × f(1)

∴ f(11) = 11 × f(1) = 55

⇒ f(1) = 5

Now, we have to calculate the value of f(1) + f(2) + f(3) + … + f(10)

= f(1) + 2f(1) + 3f(1) + … + 11f(1)

= f(1) × [1 + 2 + 3 + … + 11]

= 5 × 55

= 275

Hence, 275.

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