`S_n=1^2+2^2+3^2++n^2,ninN` then `14^2+16^2+18^2+...........+38^2`

if S_(n)=1^(2)+2^(2)++n^(2),n in N then 23^(2)+25^(2)+............+47^(2)=

What is the value of 14^2+16^2+18^2+...+30^2

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

If S_n=1^2-2^2+3^2-4^2+5^2-6^2+...... ,t h e n

Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

If S_n=1^2+(1^2+2^2)+(1^2+2^2+3^2)+ upto n terms, then S_n=(n(n+1)^2(n+2))/(12) b. S_n=(n(n-1)^2(n+2))/(12) c. S_(22)=3276 d. S_(22)=23275

S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =

If S=sum_(n=2)^oo (3n^2+1)/(n^2-1)^3 then 9/S=

If I_n=intdx/(x^2+a^2)^n,ninN , then show that: I_(n+1)=1/(2na^2)x/((x^2+a^2)^n)+(2n-1)/(2n). 1/a^2I_n