We Know,
tn = 1 + an*bn,
where
{a} = {1,2,3,4,5,...,10}, So, an = n {b} = {2,5,10, ... ,101}
Nearest elements of {b} show these element as { 1^2 + 1, 2^2 + 1, 3^2 + 1, ... ,10^2 + 1]
Thus, bn = n^2 + 1
Hence tn = 1 + an*bn = 1 + n*(n^2 + 1)
We get that,tn = 1 + n + n^3
And sum of these term is indicate by
Sn = Sum[k=1..n] (1 + n + n^3) = Sum[k=1..n] (1) + Sum[k=1..n] (n) + Sum[k=1..n] (n^3)
Sn = n + (1/2)n(n+1) + (1/4)n^2(n+1)^2
When n = 10,
S10 = 10 + 5*11 + (5*11)^2 = 10 + 55 + 3025 = 3090{ans} Safal Das Biswas Class X Savm