[" न से सिद्ध कीजिए कि : "],[qquad 1+2+3+...+n=(1)/(2)n(n+1)]

1/1.2 + 1/2.3 +…..+ 1/(n(n+1)) = n/(n+1)

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)

lim_ (n rarr oo) [(1 * n + 2 (n-1) + ... + n * 1) / (1 ^ (3) + 2 ^ (3) + ... + n ^ (3) ) +1] ^ (n)

lim_ (n rarr oo) [(1) / (n) + (n ^ (2)) / ((n + 1) ^ (3)) + (n ^ (2)) / ((n + 2) ^ (3)) + ...... + (1) / (8n)]

lim_ (n rarr oo) (1) / (n) [(1) / (n + 1) + (2) / (n + 2) + ... + (3n) / (4n)]

lim_ (n rarr oo n rarr oo) (1.n ^ (2) +2 (n-1) ^ (2) +3 (n-2) + ... + n.1 ^ (2)) / ( 1 ^ (3) + 2 ^ (3) + ... n ^ (3))

lim_ (n rarr oo) [(1+ (1) / (n ^ (2)))) (1+ (2 ^ (2)) / (n ^ (2))) (1+ (3 ^ (2) ) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2)))] ^ ((1) / (n))

1.2.3+2.3.4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….