Question -
Answer -
Let P (n) = 1/2.5 + 1/5.8 + 1/8.11 + … + 1/(3n-1) (3n+2) =n/(6n+4)
Let us check P (n) is true for n = 1
P (1): 1/2.5 = 1/6.1+4 => 1/10 = 1/10
P (1) is true.
Now,
Let us check for P (k) is true, and have to prove that P (k+ 1) is true.
P (k): 1/2.5 + 1/5.8 + 1/8.11 + … + 1/(3k-1) (3k+2) =k/(6k+4)
P (k +1): 1/2.5 + 1/5.8 + 1/8.11 + … + 1/(3k-1)(3k+2) +1/(3k+3-1)(3k+3+2)
: k/(6k+4) + 1/(3k+2)(3k+5)
: [k(3k+5)+2] / [2(3k+2)(3k+5)]
: (k+1) / (6(k+1)+4)
P (k + 1) is true.
Hence proved by mathematical induction.