Question

Assume that f(1)=0 and f(m+n)=f(m)+f(n)+4(9mn-1).for all natural no(integer>0)m and n. what is the value of f(17)?

Answer 1

Answer:

f(17) = 4832

Step-by-step explanation:

Given

f(1) = 0

f(m+n) = f(m) + f(n) + 4(9mn-1)

Therefore

f(2) = f(1 + 1) = f(1) + f(1) + 4(9×1×1 - 1) = 0 + 0 + 4 × 8 = 32

Now we can calculate f(4) as

f(4) = f(2 + 2) = f(2) + f(2) + 4(9×2×2 - 1) = 32 + 32 + 4 × 35 = 64 + 140 = 204

Similarly

f(8) = f(4 + 4) = f(4) + f(4) + 4(9×4×4 - 1) = 204 + 204 + 4 × 143 = 408 + 572 = 980

And

f(16) = f(8 + 8) = f(8) + f(8) + 4(9×8×8 - 1) = 980 + 980 + 4 × 575 = 1960 + 2300 = 4260

Therefore,

f(17) = f(16 + 1) = f(16) + f(1) + 4(9×16×1 - 1) = 4260 + 0 + 4 × 143 = 4260 + 572 = 4832

Hope this helps.