HSC Commerce (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find \[\displaystyle\sum_{r=1}^{n}r(r-3)(r-2)\].

Find \[\displaystyle\sum_{r=1}^{n}\frac{1^2 + 2^2 + 3^2+...+r^2}{2r + 1}\]

Find \[\displaystyle\sum_{r=1}^{n}\frac{1^3 + 2^3 + 3^3 +...+r^3}{(r + 1)^2}\]

Find 2 x + 6 + 4 x 9 + 6 x 12 + ... upto n terms.

Find 12² + 13² + 14² + 15² + … + 20².

Find (50² – 49²) + (48² –47²) + (46² – 45²) + .. + (2² –1²).

Find `sum_(r=1)^n(1 + 2 + 3 + . . .  + r)/r`

Find `sum_(r=1)^n  (1+2+3+....+ r)/r`

Find  `sum_(r=1)^n  (1+2+3+... + "r")/"r"`

Find n, if  `(1xx2+2xx3+3xx4+4xx5+.......+  "upto n terms")/(1+2+3+4+....+  "upto n terms") =100/3`

Find n, if `(1xx2 + 2xx3 + 3xx4 + 4xx5 + .....+ "upto n terms") / (1 + 2 + 3 + 4 +  .....+"upto n terms") = 100/3`

Find n, if  `(1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...... + "upto n terms")/(1 + 2 + 3 + 4 + ....+ "upto n terms") = 100/3`

Find n, if `(1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ...+ "upto n terms")/(1 + 2 + 3 + 4 + ...+ "upto n terms") = 100/3`

Find `sum_(r = 1) ^n (1+2+3+ ... + r)/(r)`

Find `sum_(r=1)^n (1 + 2 + 3 + ...+ r)/ r`

Find n, if `(1 xx 2 + 2 xx 3 + 3 xx 4 + 4 xx 5 + ... + "upto n terms")/(1 + 2 + 3 + 4 + ... + "upto n terms") = 100/3`

Find n, if `(1xx2 + 2xx 3 + 3xx4 + 4xx5 + ...+"upto n terms")/(1 + 2 + 3 + 4 + ...+"upto n terms") = 100/3`

Find `sum_(r=1)^n (1 + 2 + 3 + --- +r)/r`

Find n, if `(1 xx 2 + 2 xx 3 + 3 xx 4 + 4 xx 5 + ... + "upto  n terms")/(1 + 2 + 3 + 4 + ... + "upto n terms") = 100/3`.

Find `sum_(r = 1)^n (1 + 2 + 3 + ... + r)/(r)`