Question

1+2+3+4+5+6+7+8+9+10+11+12+13+14+151+16+17+18+19+20+21+22+23+24+25+26+27+28+29+39+31+32+33+34+35+36+37+38+39+49+41+42+43+44+45+46+47+48+49+50..............................................................................................................+100

Answer 1

n(n+1)/2=100(100+1)/2=50(101)=5050

Answer 2

Given,

The sum is = 1+2+3+4+....+100

To find,

The value of the given sum.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Now, the given sum is extremely large, and doing manual calculations by adding every term will be very difficult. Here, the every consecutive terms have same difference, so it will be considered as an AP series. So, we will be using the sum of the AP formula.

Here,

Number of terms (n) = 100

First term of AP (a) = 1

Common difference (d) = Second term - First term = 2-1 = 1

Sum of AP = n/2 × [2a+(n-1)×d]

= 100/2 × [(2×1) + (100-1)×1]

= 50 × (2+99)

= 50 × 101

= 5050

Hence, the final result of the given sum is 5050